MBD of Planetary Gear Mechanism using Solidworks
AIM : Constructing a Planetary gear system with four planet gears and analyzing the angular velocities for different cases.
INTRODUCTION : A Planetary gear (also known as epicyclic gear train) consists of a larger Ring gear, planet gears, and a sun gear. The sun gear is mounted at the center around which the Planet gears are mounted which can revolve around them. The planet gears are meshing internally with the Ring gear which is an internal gear. A carrier is mounted to the planet gears as shown in the image. The combination of epicycle gear trains with a planet engaging both a sun gear and a ring gear is called a planetary gear train.
Planetary gear trains provide high power density in comparison to standard parallel axis gear trains. They provide a reduction in volume, multiple kinematic combinations, purely torsional reactions, and coaxial shafting. The efficiency loss in a planetary gear train is low. This type of efficiency ensures that a high proportion (about 97%) of the energy being input is transmitted through the gearbox, rather than being wasted on mechanical losses inside the gearbox. The load in a planetary gear train is shared among multiple planets; therefore, torque capability is greatly increased. The more planets in the system, the greater the load ability and the higher the torque density.
THEORY: The method of motion of a planetary gear structure is different from traditional parallel gears. Traditional gears rely on a small number of contact points between two gears to transfer the driving force. In this case, all the loading is concentrated on a few contacting surfaces, making the gears wear quickly and sometimes crack. But the planetary speed reducer has multiple gear contacting surfaces with a larger area that can distribute the loading evenly around the central axis. Multiple gear surfaces share the load, including any instantaneous impact loading, evenly, which make them more resistant to damage from higher torque. The housing and bearing parts are also less likely to be damaged and crack from high loading.
Gear Terminologies:
Face Width: It is the length of teeth in the axial direction.
Pitch circle: When gear sets are visualized as a pair of smooth contacting discs, the pitch circles of the gear corresponds to the diameter of the discs. Pitch circles of mating gears are tangent to each other and have identical linear velocities. For this reason, pitch circles, rather than base circles, are used in many gear calculations.
Addendum: It is the height of the tooth above the pitch circle.
Dedendum: It is the depth of the tooth below the pitch circle.
Outside Diameter od Addendum Circle: The outside diameter of a gear is the diameter of the addendum (tip) circle.
Root Circle: The root circle coincides with the bottoms of the tooth spaces. It is the diameter of the dedendum circle.
Base Circle: It is the circle from which the involute portion of the tooth profile is generated.
Diametrical Pitch: The Diametral Pitch (DP) is the number of teeth per inch of diameter of the pitch circle.
Diametrical Pitch = DP=Number of teeth(n)Pitch Circle Diameter(PD)">Diametrical Pitch = DP=Number of teeth(n)Pitch Circle Diameter(PD)Diametrical Pitch = DP=Number of teeth(n)Pitch Circle Diameter(PD)
Circular Pitch: The circular pitch defines the width of one tooth and one gap measured on an arc on the pitch circle; in other words, this is the distance on the pitch circle from a point on one tooth to the corresponding point on the adjacent tooth.
Circular Pitch = CP=πDP">Circular Pitch = CP=πDPCircular Pitch = CP=πDP
Module: The module is the measure of gear tooth size which is normally used for metric system gears. The module is the pitch circle diameter divided by the number of teeth. For two gears to mesh, modules must be equal.
Module= MM =Pitch Circle Diameter(PD)number of teeth(n)">Module= MM =Pitch Circle Diameter(PD)number of teeth(n)Module= MM =Pitch Circle Diameter(PD)number of teeth(n)
Face: That part of the tooth surface lying outside the pitch surface.
Flank: The part of the tooth surface lying inside the pitch surface.
Pressure Angle: Pressure angle in relation to gear teeth, also known as the angle of obliquity, is the angle between the tooth face and the gear wheel tangent. It is more precisely the angle at a pitch point between the line of pressure (which is normal to the tooth surface) and the plane tangent to the pitch surface.
Design and Dimensions of Gears
Ring Gear
Module = 2.5
Number of teeth = 46
Pitch Diameter = 115 (After Calculations)
Sun Gear
Module = 2.5
Number of teeth = 14
Pitch Diameter = 35 (After Calculations)
Planetary Gears
Module = 2.5
Number of teeth = 16
Number of Gears = 4
Pitch Diameter = 40 (After Calculations)
Conditions for Analysis
| Sl.No | Input | Output | Fixed |
| 1 | Sun Gear | Carrier | Ring Gear |
| 2 | Ring Gear | Carrier | Sun Gear |
| 3 | Sun Gear | Ring Gear | Carrier |
MODELS of individual Gears
Sun Gear
Planet Gear
Internal Gear
Carrier
Results
1) Internal Gear(Ring gear) is fixed, Sun gear is input gear and the carrier is output.
Input
Output
Link to the animation: https://youtu.be/J0aM9PONXNc
2) Sun Gear is fixed, Internal gear(Ring gear) is input gear and the carrier is output.
Input
Output
Link to the animation: https://youtu.be/vbFyGIRAinA
3) Carrier is fixed, Sun gear is input gear and the Internal gear(Ring gear) is output.
Input
Output
Link to the animation: https://youtu.be/9-Zp0cZ3kO0
OBSERVATION
1. In the first case, the input is given to the sun gear and output is extracted at the carrier keeping the ring gear fixed, which results in the rotation of planet gear about it’s axis and enables the planetary gears to rotates .The angular velocity in this case is 280 deg/sec.
2. In the second case, the input is given to the ring gear and output is extracted at the carrier keeping the sun gear fixed. At this point we can observe peak angular velocity with 920 deg/sec , due to small size of sun and planetary gears.
3. In the third case, the input is given to sun gear , carrier is fixed and output is extracted at ring gear which results in the rotation of planet gears about their axis .Since the ring gear is bigger in diameter the angular velocity achieved is less. The angular velocity is 365.217 deg/sec.
CONCLUSION:
1. In case I; when the input is given to the sun gear and output is obtained at the carrier keeping the ring gear fixed, the planet not only rotate about their axis but are also forced to roll on the inside of the ring gear since it is fixed. This results in low speed and high torque transmitting capacity.
2. In case II; 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 quite big and planet gears are small so, when a large gear meshes with a small gear the velocity achieved from the small gear is very much because the velocity ratio is high.This is even shown in the plot of angular velocity.
3.In case III; when carrier is fixed and output is to be obtained from the ring gear the opposite happens. 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.
4. The deviations that are visible in the graphs shows that there are points where sliding is occuring between the gears while transmission.For making the graph a bit more smoother precise contact can be selected with higher values of frames per second.