Motion analysis of Planetary gear system using Solidworks MBD
Aim:- To model and perform motion analysis of planetary gear system.
Theory:- A planetary gear system, consists normally of a centrally pivoted sun gear, a ring gear and several planet gears which rotate between these. This assembly concept explains the term planetary gear system, as the planet gears rotate around the sun gear as in the astronomical sense the planets rotate around our sun.
The advantage of a planetary gear system is determined by load distribution over multiple planet gears. It is thereby possible to transfer high torques utilizing a compact design.
Given:-
- Module = 2.5
- Ring gear: Number of teeth = 46
- Sun Gear: Number of teeth = 14
- Input Speed of the Gear = 200 rpm.
- Number of planet gears = 4
Calculation:-
We know that module(m) is equal to ratio of pitch circle diameter(d) to the no. of teeth(T).
i.e. `m=d/T`
- For ring gear:-
m = 2.5
T = 46
`therefore` `d=m*T` `implies d= 2.5 **46=115`
- For sun gear:-
m = 2.5
T = 14
`therefore` `d=m*T` `implies d=2.5**14=35`
- For planet gear:-
m = 2.5
T = ?
Radius of ring gear = Radius of sun gear + Diameter of planet gear
`therefore` Diameter of planet gear = Radius of ring gear - Radius of sun gear
`implies d=(115-35)/2=40`
T = d/m `therefore`T = `40/2.5=16`
3D models:-
Gears are created using the tempalets in solidworks and defining the parameters.
Ring gear Sun gear
Planet gear
Draft & model of carrier
Features used:- Extrude, Fillet
Assembled model:-
Mates used:- Surface mate (coincident mate), Concentric mate.
Motion Analysis:-
- First the rotary motor is set at the axis of input gear and rpm is set.
- Then the solid body contacts are given and material (steel) is selected.
- Then the motion analysis is calculated and required plots are obtained.
Case 1:- Fixed: Ring gear, Input: Sun gear(200rpm), Output: Carrier.
- Angular velocity of carrier.
We can see that the initial angular velocity of carrier was 0 rad/s and later became constant to value of around 275 rad/s.
Case 2:- Fixed: Sun gear, Input: Ring gear(200rpm), Output: Carrier.
- Angular velocity of carrier.
We can see that the initial angular velocity of carrier was 0 rad/s and later became constant to value of around 900 rad/s.
Case 3:- Fixed: Carrier, Input: Sun gear(200rpm), Output: Ring gear.
- Angular velocity of ring gear.
We can see that the initial angular velocity of ring gear was 0 rad/s and later became constant to value of around 370 rad/s.
Conclusion:- From this study we can conclude that we can use planetary gear system for higher gear ratios with different cases as above. The design is compact and thus will be lighter in weight compared to traditional gear systems.
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