Planetary Gear

MOTION ANALYSIS OF PLANETARY GEAR TRAIN

AIM - To perform motion analysis of planetary gear train and plot angular velocity of output gear using Solidworks motion.

OBJECTIVE-

1. To use standard gears from Toolbox.
2. Calculate number of teeth for planetary gears.
3. To create a carrier for gear train.
4. To perform motion simulations in following conditions-

Sr. No.	Input	Fixed	Output
1	Sun gear	Ring gear	Carrier
2	Ring gear	Sun gear	Carrier
3	Sun gear	Carrier	Ring gear

1. Ring Gear
1. Module = 2.5
2. Number of teeth = 46
2. Sun Gear
1. Number of teeth = 14
3. Input Speed of the Gear = 200 rpm.
4. Number of planet gears = 4

5. To plot angular velocity of output in each case.

INTRODUCTION

A gear train is a combination of gears used to transmit motion from one shaft to another. It becomes necessary when it is required to obtain large speed reduction within a small space. The following are main types of gear train:

1. Simple gear train
2. Compound gear train
3. Reverted gear train
4. Planetary or epicyclic gear train

Planetary gear train: A gear train having relative motion of axes is called planetary gear train. In an epicyclic gear train axis of at least one of the gear moves relative to the frame.

The four basic components of the epicyclic gear train are:

1. Sun Gear: The central gear which rotates about its own axis.
2. Arm/Carrier:Holds one or more planet gears, all of the same size, meshed with the sun gear.
3. Ring or Annulus Gear:An outer ring with inward-facing teeth that mesh with the planet gear or gears. It rotates about its own axis.
4. Planetary Gear: it is positioned between the sun and ring gear and as imagined its rotation axis is going to change.

APPLICATIONS:

It is used in automatic transmissions in automobiles.

in the back gear of the lathe, hoists, pulley, blocks, wristwatches, etc.

They are also used in bicycles for controlling the power of pedaling automatically or manually.

They are also used for power train between the internal combustion engine and electric motor.

Early pencil sharpeners had a small planetary gear train.

CALCULATIONS:

Module (m) =Pitch circle diameter/Number of teeth = d/T

Diametrical pitch = 1/m

As necessary condition for gears to mate is that their module must be same. Module of each ring, sun and planetary gear is m = 2.5

RING GEAR:

Number of teeth Tr = 46

Pitch circle diameter = m*Tr = 2.5*46 = 115mm.

SUN GEAR:

Number of teeth Ts = 14

Pitch circle diameter = m*Ts = 2.5*14 = 35mm.

PLANET GEAR:

Dr = Ds+2⋅Dp

m*Tr = m*Ts+2m*Tp

46 = 14 + 2Tp

Number of teeth = 16

Pitch circle diameter = 2.5 * 16 = 40mm.

Sr. No.	Gear	Number of teeth	Pitch diameter (mm)
1	Sun	14	35
2	Ring	46	115
3	Planet	16	40

PROCEDURE

1. To create gear with help of toolbox click on Design library > Toolbox > ANSI metric > Power transmission > Gears.
2. Choose internal spur gear for ring gear and external spur gear for sun and planet gears. Using Face width = 20mm and Pressure angle = 20°. Also, put nominal shaft diameter 25 mm for planet gears and 10mm for sun gear.

1. Create a new part carrier having following top sketch.

4. Make front face of each gear coincident to right plane of assembly.
5. As we know that for the two gears to mate correctly the pitch circles of both the gears should be tangent to each other so sketch pitch circles of all gears on Right plane and mate gears concentric with them.
6. Now insert carrier in assembly and provided proper mates.
7. Enable Solidworks Motion from Tools > Add in. Click on Motion Study palette. Select Motion Analysis from Drop Down Menu.
8. Fix the ring gear.
9. Click on motor icon. By default, selection is Rotary Motor. Select sun gear in component. In Motion select Constant Speed with 200 RPM.
10. Click on Contact and make following contacts:- between spur gear and planet gear, between planet gear and ring gear and finally between planet gear and carrier.
11. Click on Motion property manager and set Frame per seconds to 1200. Select use precise contact option. Now click on Calculate.
12. Click on Plot option and create plot for angular velocity of output gear.
13. Repeat required steps for other two cases.

RESULTS -

1. Input – Sun gear, Fixed – Ring gear, Output – Carrier

The data was exported to excel and average angular velocity is calculated to be 280.1923598 deg/s

2. Input – Ring gear, Fixed – sun gear, Output – Carrier

The data was exported to excel and average angular velocity is calculated to be 919.6241894 deg/s

3. Input – sun gear, Fixed – carrier, Output – ring gear

The data was exported to excel and average angular velocity is calculated to be 366.9258134 deg/s

CONCLUSIONS -

1) Using 'Precise Contact' generates a more accurate result. Curves in the plots with precise contact fluctuate less. Moreover, the values obtained from the precise contact plot are more flexible and true.

2) As we have found angular velocities in similar way we can find torque transmitted. Hence design power transmission.

3) As seen from plot even at 1200fps there is some fluctuations which mean there will always be power loss to vibrations and wear and tear of gears.

4) In first case, planet gears are forced to rotate not only about their own axes but also around sun gear. This results in low speed and high torque transmitting capacity.

5) In second case, when ring gear is input it produces large velocity ratio and hence a large angular velocity is achieved by carrier.

6) In third case, planet gears are able to rotate only about their axes and have to transmit torque to large ring gear so, their is reduction in speed of output.

To see parts and assembly see following link:

Parts and assembly