Planetary Gear
OBJECTIVE:
To design the planetary gears. by satisfying the following conditions :
• Ring Gear o Module = 2.5 o Number of teeth = 46
• Sun Gear o Number of teeth =14
• Input Speed of the Gear = 200 rpm.
• Number of planet gears = 4
• The simulation and analysis will be done based on the following conditions:
PROCEDURE:
1)FORMULA USED:
We have three parameters i.e. pitch circle diameter. module. and a number of teeth. The formula used to calculate the module is given as:
m=d/T
Where:- m = module d = pitch diameter T = number of teeth
2) CALCULATING PARAMETERS:
FOR RING GEAR:
m = 2.5 :
T = 46 :
d = ( value we need to find) w.k.t..
d=m T d=2.546 d=115
FOR SUN GEAR:
Similarly. we can find out the pitch diameter for sun gear by using the formula.
d=35
FOR PLANET GEAR:
We need to find out pitch diameter and number of teeth. So we can find by the radius of sun and radius of inner gear (Radius of Ring Gear = Radius of Sun gear • Diameter of planet gear ).
[115 /2 = 35/2 + diameter of planet gears]
• Diameter of planet gear: d=40.Now by using the main formula we can find out the number of teeth. m=d 'T a 1.16 (Module is same for all the gears)
Results and Observation:
1. In the first case. when the input is given to the sun gear and output is obtained at the carrier keeping the ring gear fixed. the planet gear not only rotates about their axis but are also forced to roll on the inside of the ring gear along with the carrier as the Ring gear is fixed. The angular velocity obtained for this case is 279.999deg/sec and varies in a very small fraction.
2. In the second case. when the input is given to the ring gear and output is obtained from the carrier keeping the sun gear fixed. 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. The angular velocity obtained for this case is 920.00005deg/sec and varies in a very small fraction.
3. In the third case. the carrier is fixed and output is to be obtained from the ring gear with the input given to Sun gear. all the gears rotate about their axis. The planet gears rotate only about their axis and transmit motion from sun to the ring and since the ring gear is big in diameter the angular velocity achieved is less. 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 365.217 deg/sec and varies in a very small fraction.