Motion Analysis of Planetary Gear Assembly using SOLIDWORKS

Motion Analysis of a Planetary Gear Assembly using SOLIDWORKS

Gear Drives are widely used for power transmission in variety of engineering applications

Gear drives offer the following advantages compared with chain or belt drives:

1. It is a positive drive and the velocity ratio remains constant.
2. The centre distance between the shafts is relatively small, which results in compact construction.
3. It can transmit very large power, which is beyond the range of belt or chain drives.
4. It can transmit motion at very low velocity, which is not possible with the belt drives.
5. The efficiency of gear drives is very high, even up to 99 per cent in case of spur gears.
6. A provision can be made in the gearbox for gear shifting, thus changing the velocity ratio over a wide range.

Gear drives are broadly classified into four major types:

1. Simple Gear Trains
2. Compound Gear Trains
3. Reverted Gear Trains
4. Epicyclic (Planetary) Gear trains

A Planetary Gear train, which is also known as epicyclic gear train system consists of following major components:

• Ring Gear
• Sun Gear
• Planet gear
• Arm or carrier

Base on above these four components the assembly is made in-order to get the desired output specification. A simple Planetary Gear Assembly is shown in the figure below:

One of the major differences between the Planetary gear from the other three types is that planetary gear trains require two inputs in order to completely define its motion, i.e. planetary gear trains have 2 degrees of freedom, because of this availability these drives are widely used.

Important Terminologies:

• Ring Gear: It is an internal gear which covers all the gears inside of it.
• Sun gear: It is situated at the center of the assembly over which other gears rotates. Its axis is usually fixed at a position.
• Planet Gear: These are the gears which connects ring gear with the sun gear, also they are termed as planet gears because of their motion which is similar to the motion of the planets around the sun.
• Arm or Carrier: It hold the gears and prevents the failure of drive under action.

• Pitch Circle The pitch circle is the curve of intersection of the pitch surface of revolution and the plane of rotation. It is an imaginary circle that rolls without slipping with the pitch circle of a mating gear. The pitch circles of a pair of mating gears are tangent to each other.
• Pitch Circle Diameter The pitch circle diameter is the diameter of the pitch circle. The size of the gear is usually specified by the pitch circle diameter. It is also called pitch diameter. The pitch circle diameter is denoted by
• Circular Pitch The circular pitch (p) is the distance measured along the pitch circle between two similar points on adjacent teeth. Therefore,

`p= (πD)/z`

Where, `D=`Pitch Circle Diameter of Gear, `z=`No of teeth in gear

• Diametral Pitch The diametral pitch (P) is the ratio of the number of teeth to the pitch circle diameter. Therefore,

`P=z/D`

• Module The module (m) is defined as the inverse of the diametral pitch. Therefore

`m=D/z=1/P`

Problem Set: Inputs

• Ring Gear: Module = 2.5mm, Number of teeth = 46
• Sun Gear: Number of teeth = 14
• Input Speed of gear = 200 rpm
• Number of planetary Gears = 4
• Cases of operation

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

Calculations

Pitch Circle Diameter of Ring Gear `D=m×z=2.5×46=115mm`

Pitch Circle Diameter of Sun Gear `D=m×z=2.5×14=35mm`

For Planet Gear, from the below figure `R_((Rng) )=R_(sun)+D_('plant')`

`D_(plant)=115/2-35/2=40mm`

No of teeth in planet Gear `z=D/m=40/2.5=16`

Planetary Gear Calculations

Case	Carrier	Sun Gear (14 T)	Planet Gear (16 T)	Ring Gear (46 T)
1	`0`	`x`	`-(14/16) x`	`-(16)/46 (14/16 x)`
2	`y`	`x+y`	`-(14/16) x+y`	`-(16)/46 (14/16 x)+y`
3	`y`	`x+y`	`-(7/8) x+y`	`-(7/23) x+y`

Case 1: Sun Gear moving at 200 rpm (CW) and Ring Gear is fixed

`x+y=200` and `(-7)/23 x+y=0`

Solving above two cases, we get `x=153.34 (rev)/min` and `y=46.67 (rev)/min`

Thus, Speed of Carrier will be `y=46.67 (rev)/min=4.886 (rad)/sec) =280.09 (deg)/sec`

Case 2: Sun Gear is fixed and Ring Gear moves at 200 rpm (CW)

`x+y=0` and `(-7)/23 x+y=200`

Solving above two cases, we get `x=-153.34 (rev)/min` and `y=153.34 (rev)/min`

Thus, Speed of Carrier will be `y=153.34 (rev)/min=16.05 (rad)/sec)=920 (deg)/sec`

Case 3: Carrier is Fixed and sun gear is moving at 200 rpm (CW)

`y=0` and `x+y=200`

Solving above two cases, we get `x=200 (rev)/min` and `y=0`

Thus, Speed of Ring Gear will be `(-7)/23 x+y=-60.87 (rev)/min=-2.12 (rad)/sec)=-121.74(deg)/sec`

Negative sign just represents the sense of rotation of the gear, here it is seen that the ring gear rotates in opposite direction to that of the sun gear.

Parts and Assembly

• Ring Gear: Imported from ANSI Metric Tool Box with following deign parameters
  • Module = 2.5 mm
  • Face Width = 20 mm
  • No. of teeth = 46
  • Outside Diameter = 130 mm
  • Pressure Angle = 20 degrees

• Sun Gear: Imported from ANSI Metric Tool Box with following deign parameters
  • Module = 2.5 mm
  • Face Width = 20 mm
  • No. of teeth = 14
  • Nominal Shaft Diameter = 20 mm
  • Pressure Angle = 20 degrees

• Planet Gear: Imported from ANSI Metric Tool Box with following deign parameters
  • Module = 2.5 mm
  • Face Width = 20 mm
  • No. of teeth = 16
  • Nominal Shaft Diameter = 20 mm
  • Pressure Angle = 20 degrees
  • No of Gears = 4

• Carrier: Based on the Geometries of the Sun and planet Gear ,Carrier was designed as shown

Assembly

Motion Study Details:

Following Inputs were set while calculating motion Study

• Input Speed to motor = 200 rpm Constant Speed
• Precise Contacts with 120fps
• Solid Body Contacts = Steel (Dry)

Case 1:

Animation Link: https://youtu.be/QKhZFlAfvno

Case 2:

Animation Link: https://youtu.be/VTKlkkpj6Vk

Case 3:

Animation Link: https://youtu.be/bBZNkRwSD5A https://youtu.be/QaqzZhOH9o8

Conclusion

• Based on the Above study, the values obtained from calculation match with the values of the motion study.
• By Variyng the inputs in Planetary gear, we can get various combinations of speeds which is one of the most important advantage of these gear trains and is making them more useful in various applications.