Planetary Gear using Solidworks

Objective: Constructing a Planetary gear system with four planet gears and analyzing the angular velocities in different cases

THEORY: An epicyclic gear train (also known as planetary gear) 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, around the other, called the sun gear. 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.

The most basic form of planetary gearing involves three sets of gears with different degrees of freedom. Planet gears rotate around axes that revolve around a sun gear, which spins in place. A ring gear binds the planets on the outside and is completely fixed. The concentricity of the planet grouping with the sun and ring gears means that the torque carries through a straight line. Many power trains are "comfortable" lined up straight, and the absence of offset shafts not only decreases space, it eliminates the need to redirect the power or relocate other components. In a simple planetary setup, input power turns the sun gear at high speed. The planets, spaced around the central axis of rotation, mesh with the sun as well as the fixed ring gear, so they are forced to orbit as they roll. All the planets are mounted to a single rotating member, called a cage, arm, or carrier. As the planet carrier turns, it delivers low-speed, high-torque output.

Calculation

• Diameter of the Planet gear :

Radius of Ring gear(Rr) = Diameter of the Planet gear(Dp) + radius of sun gear (Rs)

Dp =Rr - Rs

Radius of Ring gear(Rr) = 0.5*Module*Number of teeths = 0.5*2.5*46 = 115/2

Radius of sun gear(Rr) = 0.5*Module*Number of teeths = 0.5*2.5*14 = 35/2

Dp=115/2 - 35/2 = 40mm

Dp = 40 mm

• Number of teeths of Planet gear:

Pitch diameter, D=m*T

T=D/m = 40/2.5 = 16

T = 16 teeths

S.No	Type of Gear	Module	Pitch Circle Diameter (mm)	Number of teeth
1.	Ring Gear	2.5	115	46
2.	Sun Gear	2.5	35	14
3.	Planetary Gear	2.5	40	16

• Outer Diameter of the Ring gear

Outer Radius of the Ring gear (Ro) = Pitch Radius of the Ring gear(Rr) + m*A

A = Addendum (Assuming A=1mm)

Outer Radius of the Ring gear (Ro) = 115/2 + (2.5*1) = 57.5 + 2.5 = 60mm

Outer Diameter of the Ring gear = 120 mm

Creating the assembly

Step:

• For the Planetary Gear analysis, We will first open the Solidworks part modelling to make the 3D CAD model of the carrier in which the planetary gears and Sun Gear are fitted.
• Then We will go for Solidworks to start the CAD model for motion analysis.
• Now we will go to design library and go for ANSI metric and then power transmission and then gears and then we will select the Spur Gears and define them and then the Internal Spur Gears for the Ring Gears.
• The process of dragging and defining the Spur Gear will be repeated 5 times as one for the Sun Gear and four times for the Planetary Gears and saving them individually as a part file.
• The process of dragging Internal Spur Gear is repeated one time and then we will define its specification as per the calculation done previously.

Then we will define the constraint such that they can only rotate about their axis. Following constaints shown in figure are used.

• We will click on Solidworks motion to go for motion analysis. Before going into cases add contact pairs. Now we will define the contact between the gears and carriers. -

1. a) 4 contact pairs - associating with a sun gear and planetary gear (material -apply dry steel)
2. b) 4 contact pairs - associating with a Ring gear and planetary gear (material -apply dry steel)
3. c) 4 contact pairs - associating with a Carrier and planetary gear (material -apply dry steel)
4. d) Contact pairs - associating with a Carrier and planetary gear (material -apply dry steel)

• Now using the motor option we will define the input as an input with 200rpm.
• Now we will hit on calculate to calculate and then using results and plots we can get our desired results and plots.

Results & Plots

Conclusion

1. In case 1, the angular velocity obtained for this case is around an avarage of 281.99deg/sec and varies in a very small fraction. This results in low speed and high torque transmitting capacity.
2. In Case 2, the angular velocity obtained for this case is around an avarage of 922.00005deg/sec and varies in a very small fraction.The angular velocity achieved is maximum since the internal gear is big and planet gears are small comparatively so when a large gear meshes with a small gear the velocity achieved from the small gear is high because the velocity ratio is high.
3. In case 3, the carrier is fixed, so the planet gears will only spin and will not revolve around the sun gear, and the output will be obtained at the ring gear which will spin in an opposite direction to the sun gear and hence a reverse gear will be obtained. The deviations that are visible in the graphs show that there are points where sliding is occurring between the gears. For making the graph more smoother we can use precise contact. The angular velocity obtained for this case is around an avarage of 362.217 deg/sec and varies in a very small fraction.