Planetary Gear
AIM - A detailed study of the planetary gear system using SOLIDWORKS Motion Analysis.
THEORY - A planetary gear system also known as the epicyclic gear train basically consist of 4 main components. The first one is the RING GEAR, which is generally an internal spur gear. The second component is the SUN GEAR which is a simple spur gear. The third one is the set of PLANETARY GEARS, these are nothing but a simple spur gears generally 3-4 in numbers. The number of planetary gears in an epicyclic gear train totally depends upon the requirement of the transmission of the Automotive System. At last is the CARRIER which connects the planetary gears with a common shaft. An epicyclic gear train is used for high torque transmissions in heavy duty machinaries and in automobile having automated transmission system.
WORKING PRINCIPLE - In an epicyclic gear train, the planetary gears transmit motion from sun gear to ring gear and vice versa. Generally there are 3 arrangements in an epicyclic gear train, these 3 arrangements are achieved by fixing one of the 3 components (i.e palnet gears, sun gear, ring gear) and leaving other two unfixed.
THE FOLLOWING ARE THE THREE CASES
| CASE | INPUT | OUTPUT | FIXED |
| 1 | SUN GEAR | CARRIER | RING GEAR |
| 2 | RING GEAR | CARRIER | SUN GEAR |
| 3 | SUN GEAR | RING GEAR | CARRIER |
CALCULATIONS
For two gears to mate effectively it is always desired to have same Module and their Pitch Circle Diamteres should always be tangent to each other
Thus,
Ring Gear
Module = 2.5mm
No. of Teeth = 46
Pitch Circle Diameter = [ Module * No. of Teeth ]
= 2.5 * 46 mm = 115mm
Sun Gear
Module = 2.5mm
No. of Teeth = 14
Pitch Circle Diameter = [Module * No. of Teeth]
= 2.5 * 14 mm = 35mm
Planet Gear
Module = 2.5mm
Pitch Circle Diameter = ?
Now from the Geometry it is very clear that
PCR of Ring Gear = PCD of Planet Gear + PCR of Sun Gear
Thus,
PCD of Planet Gear = [PCD of Ring Gear - PCD of Sun Gear ] = [115/2] - [35/2] = 40mm
Thus, No. of Teeth = [PCD of the Planet Gear / Module]
= 40/2.5 = 16 teeth
IN ALL THE THREE CASES THE PARAMETERS OF THE GEARS WOULD BE THE SAME
SETUP
CASE 1
Step 1 - Open Solidworks click on new file and choose assembly.
Step 2 - Now choose Rignt Plane and sketch as shown in the picture above. Make sure that the PC of the planet gear is tangent to PC of Ring Gear and PC of Sun Gear.
Step 3- Apply proper constrains and ensure that the sketch is fully defined( i.e, black in color). Exit the sketch.
Step 4 - Now go to Solidworks Toolbox>> ANSI Metric >> Power Transmission >> Gears
Step 5 - Choose Internal Spur Gear, drag and drop in the workspace.
Step 6 - Fill the parameters to define the size of the internal spur gear
module =2.5 mm
no. of teeth = 46
face width = 12 mm
Outer diameter = 130 mm
Step 7 - Again go to toolbox and drag and drop the spur gear.
module =2.5 mm
no. of teeth = 14
face width = 12mm
bore/ shaft diameter = 20mm
Step 8 - Choose another spur gear, this time make 4 four copies of it.
module = 2.5 mm
no. of teeth = 16
facewidth = 12 mm
bore/ shaft diameter= 22 mm
Step 9 - Apply Proper constrains and ensure that none of the component are colliding with eachother.
Step 10 - Make all the components coincident to the right plane.
Step 11 - Apply concentric mate to the following
Ring gear and bigger circle of the sketch[lock rotation]
Sun gear and the circle measuring 35mm diameter
All the four planetary gear with rest of the four circles
Step 12 - Manually mesh the gears by rotating the gears about their axis and then delete/ supress the concentric mate between the four planetary gears and the sketch.
Step 13 - Call the new part into the assembly i.e, the carrier. Assemble the carrier with the four planetary gears and lock the rotation. Mate the shaft of the carrier concentric with the sun gear.
Step 14 - Go to solidworks motion, choose motion analysis.
Step 15 - Go to motion study file properties and let the frames per second be 25(default).
Step 16 - Now choose all the components and apply contact b/w the solidbodies.
Step 17 - Go to motor and select the circular edge of the sun gear and choose 120 RPM and CW direction.
Step 18 - Go to plot choose velocity>> angular velocity >> magnitude >> choose circular face of the carrier shaft.
Run the study for 10 seconds.
CASE 2
In case 2 everything will be same as we did earlier in case 1 excpt few changes
input - ring gear
output - carrrier
fixed - sun gear
plot - carrrier
CASE 3
In case 3 there would be also some slight change as it was in case 2
input - sun gear
output - ring gear
fixed - planet gears [rotations will be unlocked but the gears will be pivoted about its axis by a concentric mate with the 4 planetary circles in the sketch]
plot - ring gear
OBSERVATIONS AND PLOT
When the motion was analysed, in all the three cases it was found that there was some fluctuation about a fixed value of angular velocity. thus it can be interpreted that when the power is being transmiited by the gears which are engaged with eachother then there are some losses in the output.
THE FOLLOWING WERE THE PLOTS THAT WERE OBTAINED IN THE THREE CASES
RESULTS
CASE 1
In case 1 from the graph it was found that the average angular velocity at output was nearly equal to 280 deg/sec.
Thus,
Input Angular Velocity = [2 'pi` RPM ]/60
= [2*3.14* 200]/60
= 20.94 rad/sec
= 20.94 * 57.3 deg/sec
= 1200 deg/sec
Hence,
INPUT SPEED at sun gear / OUTPUT SPEED at carrier = 1200/280
= 4.286 [THIS IS THE GEAR REDUCTION RATIO]
NOW,
GEAR RATIO (in first case) = 1+ [No. of Teeth on Ring Gear/No. of Teeth on Sun Gear]
= 1+ [Zr/Zs]
= 1 + [46/14]
= 4.2857
Thus our output plot is correct :)
CASE 2
In case 2 from the graph it can be interpretted that the average angular velocity at output was nearly equal to 920 deg/sec.
Thus,
INPUT SPEED at ring gear / OUTPUT SPEED at carrier =1200/920
=1.304
Now,
GEAR RATIO (in second case) = 1 + [No. of Teeth on Sun Gear/ No. of Teeth on Ring Gear]
= 1 + [Zs/Zr]
= 1 + [14/46]
= 1.3043
Thus we can say that our output is correct
CASE 3
In the last case the plot shows that the average angular velocity was somewhere around 365 deg/sec.
Thus,
INPUT SPEED at sun gear/ OUTPUT SPEED at ring gear = 1200/365
= 3.287
Now,
GEAR RATIO (in third case) = [No. of Teeth on Ring Gear/ No. of Teeth on Sun Gear]
= [46/14]
= 3.2857
Again our output is correct
CONCLUSION
Thus an epicyclic gear train can be incorporated to get various transmission ratios.
DOWNLOAD CAD FILES AND ALL THE RELEVANT MATERIALS HERE
h//drive.google.com/folderview?id=1bk3RsuscTWi5HM4LPTSQRY5hkLw4WH0x
VIDEO OF THE SIMULATION