Planetary gear analysis
Aim:
To model the various parts of planetary gear, assembled it and to analysed it in solidworks. The output parameters of various parts were also found.
Gears:
The gears play a pivotal role in the transmission system of the automobile. Many of the machines are made with the help of gears. By using the gears, we can achieve the necessary speed for the particular application. The transmission of power with higher efficiency can achieved by gear transmission than other transmission systems. Based on the application various gears are used. The various types of gears are, a) spur gear b)helical gear c)rack and pinion d)bevel gears e)miter gear f)worm and worm gear g)screw gear and h)internal gear. There are various parameters to be checked before manufacturing a gear. The various gears are assembled in a single system to transmit the enormous power.
Planetary gear:
The planetary gearing or an epicyclic gearing is an assembly of various gears to transmit the power. The planetary gearing has a sun gear at the centre and surrounded by planet gears. All this gears are enclosed in a ring gear. The major application of the planetary gearing can be seen in the lathe machines. In lathe machines, the various operation with different types of speed is achieved using the planetary gearing.
Formulae used:
- m = d/t where m=module, d=pitch circle diameter and t=number of teeth.
- Do = m(t+2) where m=module, t=number of teeth.
Input parameters:
The input parameters for the modelling of planetary gears are shown below,
- Ring Gear
- Module = 2.5 (You must use the metric system in design modeler)
- Number of teeth = 46
- Sun Gear
- Number of teeth = 14
- Input Speed of the Gear = 200 rpm.
- Number of planet gears = 4
- The carrier can be modelled based on the shaft diameters of the planetary gears.
After the modelling of planetary gear, the analysis will be done based on the following parameters,
| Sl.No | Input | Output | Fixed |
| 1 | Sun Gear | Carrier | Ring Gear |
| 2 | Ring Gear | Carrier | Sun Gear |
| 3 | Sun Gear | Ring Gear | Carrier |
In the above table, the parts which comes under the fixed category should be placed as fixed during the analysis. The parts under input parameters should be provided with 200rpm during the analysis. The angular velocity of the parts under output parameters are analysed.
Hints:
- The gear mate shouldn't used.
- The pitch circle diameter and the number of teeth of planetary gears should be found.
Calculations:
1) Outside diameter of the ring gear
Do = m(t+2)
= 2.5(46+2)
= 120m
2) Pitch circle diameter of the ring gear
d = m*t
= 2.5*46
= 115m
3) Pitch circle diameter of the sun gear
d = m*t
= 2.5*14
= 35m
4) Number of teeth of the planet gears
Radius of the ring gear = radius of the sun gear + diameter of the planet gear
d(ring)/2 = d(sun)/2 + d(planet)
We know, d = m*t
therefore, (m*t[ring])/2 = (m*t[sun])/2 + m*t[planet] (The module is the same for all the gears.)
By cancelling m on both sides,
46/2 = 14/2 + t[planet]
t[planet] = 23 - 7
t[planet] = 16
5) Pitch circle diameter of the planet gears
d = m*t (The module is the same for all the gears.)
d = 2.5*16
d = 40m.
Part modelling:
The various gear parts used in the epicyclic gear train was modelled by using the design library of solid works. The design library of the solid works have various mechanical components with different standards. The gears with ANSI metric standard is used in this analysis. All gears are made with a constant module of 2.5m
The ring gear part is modelled with 46 number of teeth, 120m of external diameter and pressure angle of 20deg.
The sun gear is modelled with 14 number of teeth and the inner shaft diameter of 20m.
The 4 planetary gears are modelled with 16 number of teeth and the inner shaft diameter of 15m.
The carrier is modelled based on the internal shaft diameter of 15m and the projections are equally placed based on the position of the planet gears.
All these parts are assembled with specific constraints and not used the gear mate.
Motion analysis:
Study - 1
In the first motion analysis, the 200 rpm input is given to the sun gear and the ring gear is being fixed. Once the analysis was done, the angular velocity of the carrier is plotted.
The parts can be fixed by pressing the right mouse button on it.
The angular velocity plot of the carrier in the study-1 is shown below,
Study - 2
The next study of motion analysis is done with providing the 200rpm input to the ring gear and the sun gear is being fixed. The angular velocity of the carrier is plotted.
Study - 3
The final study was done by fixing the carrier and an input of 200rpm is provided in the sun gear. The angular velocity of the ring gear is plotted.
Animation videos:
The motion animation video links for various case studies was provided below.
Study - 1:
Study - 2:
Study - 3:
CAD models:
The google drive link which has a CAD model of all parts, assembly and the result plot is attached below.
https://drive.google.com/file/d/1CxblaMXqfIKJzp63rs1t-VV4KSndIseF/view
Result and discussion:
From the motion analysis of the planetary gear with different input parameters, various datas can be obtained.
1) In the study - 1, the angular velocity of the carrier suddenly rises to about 300 deg/sec and maintained the angular velocity between 250 to 300 deg/sec in a pulse way. The angular velocity lies in the value of 275 deg/sec.
2) In the study - 2, the angular velocity of the carrier suddenly rises to 950 deg/sec. It maintained the angular velocity in between 850 t0 950 deg/sec. The angular velocity gradually lies in the 900 range.
3) From the above two case studies, it was obtained that the angular velocity of the carrier has a maximum value when the sun gear is fixed and the input of 200rpm is given to the ring gear.
4) The angular velocity of the ring gear is initially rises to about 420 deg/sec in the study - 3. The angular velocity maintained in a pulse rate of values between 350 to 400 deg/sec.
Conclusion:
Thus the planetary gearing was modelled and the motion analysis was performed with different parameters.
Reference: