MBD simulation of a Planetary Gear Train in Solidworks

Aim:

To perform MBD simulation on a Planetary Gear Train in Solidworks.

Objective:

• To model and assemble the gear train.
• To perform motion analysis for different conditions.
• To analyse the resulting plots.

Theory:

Epicyclic gearing or planetary gearing is a gear system consisting of one or more outer, or planet, gears or pinions, revolving about a central sun gear or sun wheel. Typically, the planet gears are mounted on a movable arm or carrier, which itself may rotate relative to the sun gear. Epicyclic gearing systems also incorporate the use of an outer ring gear or annulus, which meshes with the planet gears. Planetary gears (or epicyclic gears) are typically classified as simple or compound planetary gears. Simple planetary gears have one sun, one ring, one carrier, and one planet set. Compound planetary gears involve one or more of the following three types of structures: meshed-planet (there are at least two more planets in mesh with each other in each planet train), stepped-planet (there exists a shaft connection between two planets in each planet train), and multi-stage structures (the system contains two or more planet sets). Compared to simple planetary gears, compound planetary gears have the advantages of larger reduction ratio, higher torque-to-weight ratio, and more flexible configurations.

The axes of all gears are usually parallel, but for special cases like pencil sharpeners and differentials, they can be placed at an angle, introducing elements of bevel gear (see below). Further, the sun, planet carrier and ring axes are usually coaxial.

Epicyclic gearing is also available which consists of a sun, a carrier, and two planets which mesh with each other. One planet meshes with the sun gear, while the second planet meshes with the ring gear. For this case, when the carrier is fixed, the ring gear rotates in the same direction as the sun gear, thus providing a reversal in direction compared to standard epicyclic gearing.

We will be conducting the study under the following conditions:

Specifications of Gears:

Sun Gear: m = 2.5, T = 14

Ring Gear: m = 2.5, T = 46

Planet Gear Dimensions:

To determine the specifications of the planet gear, A sketch is created containing the pitch circle diameter of the sun and ring gear whose dimensions are known.

Then an arbitrary circle is created and is is given tangent constraints to both sun and ring gear circles. This is the because the gear law needs to be satisfied. On measuring, the pcd of planet gear turns out to be 40 mm.

Using the relation P = mT,

Where, m = module & T = number of teeth, the number of teeth of planet gear was found out to be 16. This was the used to completely define the planet gear and make the part file.

Setup Explanation:

1. First, the components are modelled as per known dimensions as shown. The carrier is modelled depending on the shaft diameter of planet gears.

2. Then the model is assembled using appropriate mates as shown.

3. Using the move tool, the gears are moved and positioned such that they are not touching each other.
4. With the Solidworks motion add-in enabled, click on motion study 1 and then click on motion analysis.
5. Add a motor to the axis of the Sun gear as shown. Set constant speed to 200 rpm.

6. Set contacts between each pair of solid bodies as per logic and set material to steel (dry).
7. Fix the Ring gear.
8. Go to settings and set frame rate to 1200 frames per second and also enable precise contacts for accurate analysis.
9. Set key point time to 1 second for faster calculation time.
10. Hit calculate and wait for the analysis to complete.
11. Insert plot for the angular displacement of the ring gear.
12. Do the above processes for 2 more cases as mentioned above.

Results:

1. Case 1:

• Input rotation is given to sun gear, output is taken from carrier and the ring gear is fixed.
• Result:

• Animation: https://youtu.be/xVCdT66aATM

2. Case 2:

• Input rotation is given to ring gear, output is taken from carrier and the sun gear is fixed.
• Result:

• Animation: https://youtu.be/6aQAZFQDlnc

3. Case 3:

• Input rotation is given to sun gear, output is taken from ring gear and the carrier is fixed.
• Result:

• Animation: https://youtu.be/oLFIDVzEFbw

Observations:

1. In case 1, the angular velocity of carrier is constant and is approximately equal to 278 rpm. The slight deviations are error due to gear backlash.
2. In case 2, the angular velocity of carrier is constant and is approximately equal to 920 rpm. The slight deviations are errors due to gear backlash.
3. In case 3, the angular velocity of ring gear is constant and is approximately equal to 360 rpm however the direction is opposite to input. The slight deviations are errors due to gear backlash.

Conclusions:

1. In case 1, at the point of contact between the sun and the planet gear the velocity will be same , but at a point where the planetary gear is in contact with the ring gear the velocity should be zero .So to satisfy this, the planet gear should spin as well as turn simultaneously to satisfy both these conditions. The obtained output velocity is the velocity of revolution of carrier which satisfies this condition.
2. In case 2, the input is ring gear and the sun gear is fixed, the ring gear will rotate the planet gear and the point of contact between the planet and ring gear should have the same velocity and also the velocity of mating point of sun and planet gear should be zero, so to satisfy this, the planet gear will spin as well as turn. But the output obtained will be more as compared to case 1 since the radius of ring gear is bigger than sun’s as can be seen from the plot.
3. In case 3, the carrier is fixed, so the planet gears will only spin and will not revolve around the sun gear, behaving like a simple gear train 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.

File Link: https://drive.google.com/open?id=1uVe_8OaYa45HqO_Od1HMLQ5oZFs_H3r9