Planetary Gear

REPORT ON MOTION ANALYSIS OF PLANETARY GEAR

AIM – To conduct the motion analysis of the Planetary gear setup, generate and explain the plots for the given conditions.

BODY OF THE CONTECT.

• CONDUCT MOTION ANALYSIS

• Creating Assembly

As the gears that will be used for making planetary gears assembly are to be imported from the solidwork’s toolbox. There is a need to model only one part named planetary gears carrier separately in the part interface of the solidworks.

Before importing the gears there is a need to finalize the specifications of the gears which are given as follows.

For Ring gear

Moduie (M) = 2.5

No. of teeth = 46

For Sun gear

Module (M) = 2.5

No. of teeth = 14

The pitch circle diameter for both the gears can calculated from the formula given below.

`(M) = frac{P.C.D}{Number of teeth}`     ……………. {1}

where M = module

P.C.D. = Pitch circle diameter

Hence, from above formula the Pitch circle diameter for Ring gear and Sun gear are 115mm and 35mm respectively. This data can be used to find the Pitch circle diameter of Planetary gear.

Through modeling in the solidworks it is possible to find the Pitch circle diameter of Planetary gear as shown in above image.

Hence, For Planetary gear

Module (M) = 2.5      [ it is same for all gears]

Pitch circle diameter = 40 mm

So, by using formula {1}

No. of teeth = 16

Gear Specifications

	No. of teeth	P.C.D	Module
Ring gear	46	115	2.5
Sun gear	14	35	2.5
Planetary gear	16	40	2.5

The above gear data can be used to import gears from solidworks toolbox.

• The next step is to assemble the gears as per the P.C.D. Drawing.

• Modelling the planetary gears carrier as per internal diameter of planetary gear.

• Complete Assembly of the Planetary gear setup

• Conduct Motion Analysis

After the assembly is completed the next step is to conduct the Motion analysis of the setup. It helps to understand the behaviour of any mechanical system under actual conditions.

• Conditions for Motion Analysis

1. Input speed = 200 rpm
2. No use of Gear mate
3. Input parameters

Sr. no	Input	Output	Fixed
1	Sun gear	Carrier	Ring gear
2	Ring gear	Carrier	Sun gear
3	Sun gear	Ring gear	Carrier

The Motion Analysis is been conducted for four seconds.

• RESULTS

• Angular Velocity of Carrier when Ring gear is in fixed condition.

The above graph show the Angular Velocity in deg/sec of Planetary gears Carrier by giving input rotation to the sun gear and keeping Ring gear fixed with respect to time. From the above graph it can be seen that for given gear specification if the sun gear is rotated at 200 rpm and ring gear is kept fixed then planetary gears carrier will rotate with an angular velocity of approximately around 280 deg/sec which will be converted to rpm in following formulas

  1 rad = 57.2958 deg

`omega = frac{2 pi N}{60}`             ……………….{2}

Where,  `omega`= Angular velocity in rad/sec

N = Revolution per minute

From the above formulas the speed of the Carrier is approximately around 46 rpm. Hence it can be seen that there is reduction in the output speed as compare to the input speed of the system and also it can observed  that the speed is not uniform throughout the study. The upward and downward races can be seen in the plot that shows the fluctuation in the speed throughout the study.

• Angular Velocity of Carrier when Sun gear is in fixed condition.

The above graph show the Angular Velocity in deg/sec of Planetary gears Carrier by giving input rotation to the sun gear and keeping Ring gear fixed with respect to time. In this case when Sun gear is fixed and input given to the Ring gear the angular velocity of the planetary gear carrier is shown by the graph is approximately around 920 deg/sec i.e. around 153 rpm by using formulas {2}

So it can be seen that there is less reduction in the output  speed as compare to the first case.

• Angular Velocity of Ring gear when Carrier is in fixed condition.

The above graph show the Angular Velocity in deg/sec of Ring gear by giving input rotation to the sun gear and keeping Carrier fixed with respect to time. From the graph the value of angular velocity of Ring gear can be seen around 370 deg/sec i.e. around  61.65 rpm using formulas {2} .  The plot is not completely uniform there is a fluctuation in speed can be seen from the plot.

So, if all three plots are compared together then it can be observed that in first case the reduction in the speed at output is less as compare to other two cases which also means that the amount of torque applied will be grater in first case as compare to other two cases. Hence, first case will be more appropriate for the application that require more amount of torque.

CONCLUSION = From the entire challenge it can be concluded that the motion analysis in case of gear transmission is extremely important which helps to accurate positioning of the gears with considering its dynamic behaviour.