Planetary Gear

Aim :- Designing the Planetary Gear and show its motion analysis .

Given : -

• Ring Gear
  • Module = 2.5 (You must use the metric system in design modeler)
  • Number of teeth = 46
• Sun Gear
  • Number of teeth = 14
• Input Speed of the Gear = 200 rpm.
• Number of planet gears = 4

Planetary Gear

An planetary gear (also known as epicyclic gear train ) consists of two gears mounted so that the center of one gear revolves around the center of the other. A carrier connects the centers 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.An epicyclic 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 .

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.

Calculations

• Ring gear
  
  • Module(m) = 2.5
  • Number of teeth(T) = 46
  • Pitch circel diameter (PDC) = module * number of teeth = 2.5 * 46 = 115
• Sun gear
  • Module = same as ring gear = 2.5
  • Number of teeth = 14
  • Pitch circel diameter (PDC) = 2.5 * 14 = 35
• Planet Gear
  • Pitch circel radius of ring = Pitch circel radius of sun gear + Pitch circel diameter of planet gear
  • 115/2 = 35/2 + PCD of planet gear i.e PDC of planer gear is 40
  • Number of teeh = PDC / m = 40/2.5 = 16

Gear	Pitch circel diameter (PDC)	Number of teeth	Module
Ring gear	115	46	2.5
Sun gear	35	14	2.5
Planet gear	40	16	2.5

Designing the Planetary Gear

• For gears go to Design library -> Toolbox ->ANSI Metric ->Power Transmition -> Gears and then drag the required gear and give dimension to gear

• Ring Gear

• Planet gear

• Sun gear

• Carrier

• Planetary Gear
  • Import all the components .
  • Draw the pitch circel of sun and ring gear in right plane and add concentric mate with repective gear
  • Coincident sun and ring gear with right plane
  • Add coincentric mate between the output shaft of the carrier and the sun gear and between the arms of carrier and planet gears
  • Coincident all 4 planet gear and carrier with right plane

Motion Analysis

Case 1

Input :- Sun gear

Output :- Carrier

Fixed :- Ring gear

Animation

Case 1

Angular Velocity of output

in case 1 when we give 200rpm to the input sun gear keeping the ring gear fixed and taking output from carrier , the sun gear rotate at 200 rpm with the help of input motor and rotate the planet gear

Case 2

Input : -Ring Gear

Output : -Carrier

Fixed : - Sun gear

Animation

Case 2

Angular velocity of output

Case 3

Input : -Sun gear

Output :- Ring gear

Fixed : - Carrier

Animation

Case 3

Angular velocity of output

Solidworks files

• Carrier Aman_carrier
• Planet gear Aman_planet_gear
• Ring gear Aman_ring_gear
• Sun gear Aman_sun_gear
• Planetary gear assembly Aman_planetary_gear

Result

Calculations

Let the rpm of sun gear is x so according to the gear ratio the rpm of planet gear is (14/16)x rotating in the opposite direction and the rpm of ring gear is (14/46)x rotating in the opposite direction from sun gear and if we add carrier rpm whitch is assume to the y is it going to add in all three gear

Rpm of sun gear is x+y

Rpm of planet gear is -(14/16)x + y

Rpm of ring gear is -(14/46)x + y

Note : - If two gear is in contact the rotio of there rpm is the resiprocal of the ratio of there number of teeth

Case 1 : - In case 1 when we give 200rpm to the input sun gear keeping the ring gear fixed and taking output from carrier .

x+y = 200 (Input) -(14/46)x + y = 0 (Fixed gear) Solving the two equations we can get y =46.67

Carrier rotates at 46.67rpm which is 280degree/sec

Case 2 : - In the case 2 when we fixed the sun gear and give input of 200rpm to ring gear and taking rpm from carrier

x+y = 0 (sun gear fixed) -(14/46)x+y = 200 (Input to ring gear) Solving the above two equations we can get y = 153.33

Output carrier rotates at 153.33rpm which is 920degrees/sec

Case 3 : - In case 3 we give input to the sun gear taking output from ring gear kepping the carrier as fixed

x+y = 200 (Input to the sun gear) y = 0 (carrier is fixed)

Solving the above two equation we can get rpm of ring gear is 60.86 which is 365degrees/sec

The result obtained from the plot of motion study in solidworks is giving approximately same value as we obtained from the theoretical calculations , the variation in the speed from actual values can we due to the various dynamic factors like inelastic collision in gears ,due to various gears terminology like backlash ,teeth profile etc

This result can be modified by some amount if we use precise contact and increase number of frames per second but it will increase the calculation time.