Motion Analysis on Planetary Gear System in SOLIDWORKS

Aim: Study motion analysis of planetary gear system using SOLIDWORKS.

Objectives:

• Calculate the pitch circle diameter and the number of teeth for the planet gear.
• Perform motion analysis.
• Explain Planetary gear system.
• Discuss the plots obtained.

Inputs:

• 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

Problem Statement:

With the above input parameters, we are going to run a simulation on the following cases,

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

Theory:

A 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. 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.

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. 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.

Epicyclic gears get their name from their earliest application, which was the modelling of the movements of the planets in the heavens. Believing the planets, as everything in the heavens, to be perfect, they could only travel in perfect circles, but their motions as viewed from Earth could not be reconciled with circular motion.

Governing Equation:

`"Module=(Pitch Circle Diameter)/(Number of Teeth)"`

Calculations:

For Number of teeth in Planet Gear,

For given problem we can write,

Diameter of Ring Gear (D_r) = 2*Diameter of Planet Gear (D_p) +Diameter of Sun Gear (D_s)

From governing equation, we can write above equation as- `mTr=2*mTp+mTs`

Here, `m` = Module (same for all gear)

`Tr` = Number of teeth in Ring Gear

`Tp` = Number of teeth in Planet Gear

`Ts` = Number of teeth in Sun Gear

`2*Tp=Tr-Ts=46-14=32`

`"Therefore, Number of teeth in Planet Gear (Tp)=16"`

For Pitch Circle Diameter for Planet Gear,

We know that, `m=("pitch circle diameter of planet gear" (Dp))/("number of teeth in planet gear" (Tp))`

Therefore, `Dp=2.5*16=40 mm`

Procedure:

All the gears are added from the toolbox library. All units are in MMGS. Pressure Angle is 20 for all gears.

Ring Gear-

Module = 2.5; Number of teeth = 46; Width = 20; Outside Diameter = 130

Sun Gear-

Module = 2.5; Number of teeth = 14; Width = 20; Shaft Hole Diameter = 15

Planet Gear-

Module = 2.5; Number of teeth = 16; Width = 20; Shaft Hole Diameter = 15

Carrier-

Assembly-

Following Mates are provided:

Axis of carrier is mated with front and top plane

Face of carrier is mated with right plane

All the gears are mated with right plane with distance of 30mm

The 4 shafts of carrier are made concentric with four planetary gear

Axis of sun gear is mated with front and top plane

Face of sun gear is mated with right plane with 30mm distance

All the gears are adjusted such that they not create interference with each other. (Interference check is done for assurance)

Motion Analysis –

In Motion study properties option 25fps and use precise contact are selected

3 Body contact are provided viz. 1) between Sun and Planetary gears, 2) Planetary gears and Ring gear, 3) Planetary gear and Carrier. Steel (Dry) material is selected for all components.

Time for motion study is adjusted to 10 sec

Now we have to study 3 cases, in each case one component is taken as input, one is taken as output and the remaining one is fixed.

A component is fixed by selecting the component in tree, right clicking on it and selecting fix option in each case. For motion study 1,2 & 3; Ring gear, sun gear and carrier are fixed respectively.

By enabling show axis option, we select the axis of the component which has to be taken as input in each of the cases. Motor is provided on input component’s axis in each case. RPM provided is 10 rpm. For motion study 1,2 & 3 motor is provided on Sun gear, Ring gear, Sun gear axis respectively.

In results option, Displacement/Velocity/Acceleration->Angular Velocity->Magnitude is selected. It will provide us with output which is angular velocity plot. For motion study 1,2 & 3 Carrier, carrier and Ring gear are selected respectively.

Result:

Case 1

Input: Sun Gear Output: Carrier Fixed: Ring Gear

In case study 1, the ring gear is fixed and input is provided on sun gear and output is obtained at carrier. In this case the force provided by sun gear is transmitted to carrier through planetary gears while the ring gear remains fixed in its position.

Case 2

Input: Ring Gear Output: Carrier Fixed: Sun Gear

In case study 2, the sun gear is fixed and input is provided on ring gear and output is obtained at carrier. In this case the force provided by ring gear is transmitted to carrier through planetary gears while the sun gear remains fixed in its position.

Case 3

Input: Sun Gear Output: Ring Gear Fixed: Carrier

In case study 3, the ring gear is fixed and input is provided on sun gear and output is obtained at carrier. In this case the force provided by sun gear is transmitted to ring gear through planetary gears while the ring gear remains fixed in its position.

Conclusion: Comparing the angular velocity plot of above three case study we observe that

Angular velocity transmitted from sun to carrier when ring gear is fixed is low with slight fluctuation. The RPM obtained at output is also low.

Angular velocity transmitted from ring gear to carrier when sun gear is fixed is high with slight fluctuation. The RPM obtained at output is moderate.

Angular velocity transmitted from sun gear to ring gear when carrier is fixed is constant with no fluctuation. The RPM obtained at output is high.

Project Links:

CAD files Google Drive Link

YouTube Video Link of Case Study – One , Two , Three

References:

https://www.engineersedge.com/gear_formula.htm

http://www.thecatalystis.com/gears/

A Textbook of Machine Design by R.S. Khurmi