Planetary Gear

Aim:

Modelling Planetary Gear mechanism and calculating angular velocity with fixing by fixing the sun gear, ring gear and Carrier separately with help of motion analysis

Introduction:

A planetary gear set (also known as an epicyclic gear train ) consists of two gears mounted so that the centre of one gear revolves around the centre of the other. A carrier connects the centres of the two gears and rotates to carry one gear, called the planet gear or planet pinion, around the other, called the sun gear or sun wheel. The planet and sun gears mesh so that their pitch circles roll without slip. A point on the pitch circle of the planet gear traces an epicycloid curve. In this simplified case, the sun gear is fixed and the planetary gear(s) roll around the sun gear.

Theory:

A planetary gear train can be assembled so the planet gear rolls on the inside of the pitch circle of a fixed, outer gear ring, or ring gear sometimes called an annular gear. In this case, the curve traced by a point on the pitch circle of the planet is a hypocycloid.

The combination of epicycle gear trains with a planet engaging both a sun gear and a ring gear is called a planetary gear train. In this case, the ring gear is usually fixed and the sun gear is driven.

Benefits

Planetary gear trains provide high power density in comparison to standard parallel axis gear trains. They provide a reduction in volume, multiple kinematic combinations, purely torsional reactions, and coaxial shafting. Disadvantages include high bearing loads, constant lubrication requirements, inaccessibility, and design complexity.

The efficiency loss in a planetary gear train is typically about 3% per stage. This type of efficiency ensures that a high proportion (about 97%) of the energy being input is transmitted through the gearbox, rather than being wasted on mechanical losses inside the gearbox.

The load in a planetary gear train is shared among multiple planets; therefore, torque capability is greatly increased. The more planets in the system, the greater the load ability and the higher the torque density.

The planetary gear train also provides stability due to an even distribution of mass and increased rotational stiffness. Torque applied radially onto the gears of a planetary gear train is transferred radially by the gear, without lateral pressure on the gear teeth.

Basic components

The three basic components of the epicyclic gear are:

• Sun: The central gear
• Carrier: Holds one or more peripheral Planet gears, all of the same size, meshed with the sun gear
• Ring or Annulus: An outer ring with inward-facing teeth that mesh with the planet gear or gears

Requirements of planetary gear mechanism 

Use the following inputs for designing the Planetary Gear

• Ring Gear
  • Module(z) = 2.5 (You must use the metric system in the design modeller)
  • Number of teeth = 46
• Sun Gear
  • Number of teeth = 14
• Input Speed of the Gear = 200 rpm.
• Number of planet gears = 4
• The module is the same for all the gears

The dimensions of the carrier depending on the shaft diameter of the planet gear.

Access design library

Ring gear for library

Sun gear from libray

let's calculate

no. of teeth for planet gear 

The first constraint for a planetary gear to work out is that all teeth have the same pitch or tooth spacing. This ensures that the teeth mesh.

The second constraint is:
    R = 2 × P + S

here,

R = 46

S = 14

Now,  2P=46-14

P=32/2

P = 16

planetary gear should be 16 teeth as per Calculation.

Pitch circle diameter 

The pitch circle diameter is d = zm

(where z = number of teeth, m = module)

d = 2.5*16

d = 40 units

The Pitch circle diameter of the planetary gear is 40mm

Planetary gear from the library

Carrier 3d part as per required

Assembled back view 

Assembled front view

Now run the mechanisms with 3 different conditions 

here, 

Input  is given as 200 RPM and output also will get as some RPM

Condition 1

The ring gear is fixed, the sun gear is driven by external sources and output will get from Carrier. 

The animation file is saved in the attachment section

The Carrier angular velocity in the condition

Condition 2

The Sun gear is fixed, the Ring gear is driven by external sources and output will get from Carrier.

The animation file is saved in the attachment section.

The Carrier angular velocity in the condition

Condition 3

The carrier is fixed, the sun gear is driven by external sources and the output will get from the Ring gear.

The animation file is saved in the attachment section.

The ring gear angular velocity in the condition

Results and explanation:

In the first condition, the carrier's angular velocity is 287deg/sec when the sun gear rotates with 1200deg/sec as ring gear is fixed. Then the speed ratio is approx. 4.1:1

In the second condition, The angular velocity of the carrier is 933deg/sec when the ring gear rotates with 1200deg/sec as sun gear is fixed. Then the speed ratio is approx. 1.3:1

In the third condition, The angular velocity of the ring gear is 376/sec when the sun gear rotates with 1200deg/sec as the carrier is fixed. Then the speed ratio is approx. 3.2:1

Observation and the conclusion:

Planetary gear trains provide high power density in comparison to standard parallel axis gear trains. They provide a reduction in volume, multiple kinematic combinations, purely torsional reactions, and coaxial shafting. Disadvantages include high bearing loads, constant lubrication requirements, inaccessibility, and design complexity.