PLANETARY GEAR

MOTION ANALYSIS OF EPICYCLIC / PLANETARY GEAR TRAIN

CONTENTS

1. AIM
2. INTRODUCTION
   1. Basics of gear
      Spur gear terminology
      Some geometric relationships
   2. Gear train
      Epicyclic gear train
3. INPUTS FOR DESIGN OF VARIOUS GEARS
   Calculation for the no. of teeth, z(p) & pitch circle diameter, d(p) of the planetary gear
4. THE DESIGN PROCESS
5. THE ASSEMBLY
6. THEORY ON MOTION STUDY
7. MOTION STUDY 1
   Observations & conclusions 1
8. MOTION STUDY 2
   Observations & conclusions 2
9. MOTION STUDY 3
   Observations & conclusions 3

AIM

To successfully create, assemble and run the motion analysis for the epicyclic / planetary gear train in SOLIDWORKS as per the following cases shown.

	Fixed	Input	Output
Case 1	Ring Gear	Sun Gear	Carrier
Case 2	Sun Gear	Ring Gear	Carrier
Case 3	Carrier	Sun Gear	Ring Gear

And plot the graph for angular velocities with respect to time for the output components in each case.

INTRODUCTION

Basics of Gear:

Spur gear terminology:

P	=	Diametral pitch
z	=	Number of teeth
d	=	Pitch circle diameter
m	=	Module
p	=	Circular pitch
a	=	Addendum
b	=	Dedendum
c	=	Clearance = (b-a)
do	=	Outside diameter (or) Diameter of addendum circle

The module ‘m’ is the ratio of the pitch diameter to the number of teeth on the gear. The unit of module in SI system is mm. The diametral pitch P is the ratio of the number of teeth on the gear to its pitch circle diameter. It is the reciprocal of module. The diametral pitch is usually expressed as ‘teeth per inch’.

The addendum circle (visible on a gear) is the largest circle on the gear. The addendum ‘a’ is the radial distance between the pitch circle and the addendum circle. The dedendum circle (visible on a gear) is usually the smallest circle on the gear. The dedendum ‘b’ is the radial distance between the pitch circle and the dedendum circle. The dedendum is larger than the addendum; i.e., b > a. The depth of tooth ‘h’ is the sum of the addendum and dedendum; i.e., h = (a + b).

The base circle or clearance circle of a gear is tangent to the addendum circle of its meshing gear. The clearance ‘c’ is the difference between the dedendum 'b' and addendum 'a' of the gears.

Some geometric relationships:

m	=	d/z
P	=	z/d = 1/m
p	=	(`pi`d)/z = `pi`m = `pi`/P
p*P	=	pi

Conjugate action:

The gears must be designed such that the ratio of rotational speeds of driven and driver gear is always constant. When the tooth profiles of two meshing gears produce a constant angular velocity during meshing, they are said to be executing conjugate action. That is,

(ω1 / ω2) = constant

Gear Trains:

A combination of gears employed to transmit motion from one shaft to other(s) is called ‘Gear train’.

Gear trains are classified into the following:

1. Simple gear trains.
2. Compound gear trains.
3. Reverted gear trains.
4. Epicyclic (or planetary) gear trains

Epicyclic gear train:

Epicyclic gear train is the one in which the axes of some of the gears have motion. The said gear(s) would be revolving about external axis or axes. Whereas in other gear trains, the axes of all the gears do not have motion, only the gears rotate on their axes. Planetary gear trains are often employed to make more compact gear reducer (large speed reduction in a small volume) compared to other gear trains. Multiple kinematic combinations (multiple inputs) are possible with planetary gear trains. Since few gears are revolving around, the bearings are subjected to high loads; requiring constant lubrication. Hence, planetary gears are placed in box with lubricants, sometimes in a sealed box inaccessible to maintenance crew. Their design and manufacturing is complex and require a very high degree of balance.

An epicyclic gear train with one degree of freedom is as shown below. The sun gear A is grounded. In other words, it is held stationary. The arm/lever is pivoted on the axis of gear A and on its other end it carries a planetary gear B. The gear B is meshing with the sun gear A. As the arm rotates, the planetary gear B revolves around the periphery of the gear A and also rotates on its axis since it is meshing with the sun gear A. The gear B is the output gear. Since the sun gear is grounded, the gear B gets its input only from the rotation of arm. This is called ‘one degree of freedom’.

Another important application of the planetary gear train is to make use of two degrees of freedom of this mechanism when the sun gear is released from the ground. This two-degrees-of-freedom mechanism requires two input conditions to determine completely the motion of gear train. The two-degrees-of-freedom mechanism allows two separate input speeds to be combined to give an output speed proportional to the sum or difference of the two inputs. Two degrees of freedom is used in roving and combing machines and auto-levellers. Using two or more degrees of freedom PIV (Positively Infinitesimally Variable) drives can be constructed. The input speeds are preciously controlled by speed-control motors to vary the output speed infinitesimally and if requires continuously also.

Some applications of Epicyclic Gear Train:

1. Automatic transmissions in automobiles.
2. Power train between internal combustion engine and an electric motor.
3. In bicycles for controlling power of pedalling automatically or manually.

INPUTS FOR DESIGN OF VARIOUS GEARS

Given:

Module, m = 2.5

No. of teeth on Ring Gear, z(r) = 46

No. of teeth on Sun Gear, z(s) = 14

No. of Planet Gears, n(p) = 4

Calculation for the no. of teeth & pitch circle diameter of the planetary gear i.e., z(p) & d(p) respectively:

Since, there is one Sun Gear, one Ring Gear and four Planetary Gears, these could be mated as follows:

From above we can clearly see that,

d(r) = d(p)+d(s)+d(p)

Therefore,

d(p) = {d(r)-d(s)}/2 ............................................. equation (i)

Also, we know from our introduction that in order to satisfy the law of gearing, the module of two mating gears must be same. Since in our case, all the gears are meshed to each other therefore, all the gears have the same module. that is,

m = m(r) = m(s) = m(p)

m = d(r)/z(r) = d(s)/z(s) = d(p)/z(p)

2.5 = d(r)/46 = d(s)/14 = d(p)/z(p) ..................... equation (ii)

Calculating the values,

d(r) = 115 mm

d(s) = 35 mm

Substituting in equation (i),

d(p) = {(115)-(35)}/2

d(p) = 40

Thus, the pitch circle diameters of all the gears is as shown below.

Also, from equation (ii)

2.5 = 40/z(p)

z(p) = 16

Thus,

the no. of teeth on the Planetary Gear, z(p) = 16 and,

the pitch circle diameter of the Planetary Gear = 40 mm.

	Module, 'm'	Pitch circle diameter, 'd'	No. of teeth, 'z'
Ring Gear	2.5	115	46
Sun Gear	2.5	35	14
Planetary Gear	2.5	40	16

THE DESIGN PROCESS

The design process refers to the creation of all the parts for the required planetary gear assembly. This generally starts by dragging and dropping of the gears from the SOLIDWORKS design library and changing their configurations. To access the gears from the design library use the following sequence.

Design Library

>>

Toolbox

>>

ANSI Metric

>>

Power Transmission

>>

Gears

Note that we have used the ANSI Metric standards since we have been provided with the module. In case we had been provided with the diametral pitch value, it would have been easy to use the ANSI Inch standards. In either case the relation between module and the diametral pitch as shown below can be used for the conversion of the values.

P

=

z/d = 1/m

The various parts with their names and configurations are as shown below.

Rupesh_1_Ring_Gear.SLDPRT

Rupesh_2_Sun_Gear.SLDPRT

Rupesh_3_Planetary_Gear.SLDPRT

Rupesh_4_Carrier.SLDPRT

Note:

The dimensions of the carrier depend on the shaft diameter of the planet gear.

Pressure angles for all the gears is 20 degrees.

Face width for all the gears is 10 mm.

The outside diameter of the ring gear is 134 mm.

The nominal shaft diameter for the planetary gears is 20 mm and for the sun gear is 18 mm.

THE ASSEMBLY

Note:

We haven't used the gear mates. But, keeping the position of each gear such that the teeth do not overlap each other. This can be achieved by the 'Move Component' tool under the 'Assembly' tab of the SOLIDWORKS.

Theory on Motion Study:

Motion study is the graphical simulation of motion for assembly models. Here, by motion study we are generally referring to a motion analysing in the SOLIDWORKS. Motion analysis is used for accurately simulating and analyzing the effects of motion elements (including forces, springs, dampers, and friction) on an assembly. It uses computationally strong kinematic solvers, and accounts for material properties as well as mass and inertia in the computations. We will use motion analysis to plot simulation results for further analysis.

To establish the Motion Analysis in SOLIDWORKS, make sure that the 'SOLIDWORKS Motion' under the 'SOLIDWORKS Add-Ins' tab is enabled. If in some cases, the 'SOLIDWORKS Add-Ins' tab is not visible, right-click on any of the tabs, say Assembly and that's where you can enable or hide the tabs as per the convenience. After you have successfully enabled the 'SOLIDWORKS Motion' click on the 'Motion Study 1' at the bottom and make sure you change 'Animation' to the 'Motion Analysis'. Now we are ready to move and set up the motor, contacts and plot various graphs as per the requirements.

MOTION STUDY 1

Motion Study 1 refers to the Motion Analysis of the Planetary Gear Assembly (i.e., Rupesh_Final_Assem.SLDASM) for the Case 1.

	Fixed	Input	Output
Case 1	Ring Gear	Sun Gear	Carrier

Step 1: Fixing the Ring Gear (i.e., Rupesh_1_Ring_Gear):

1. Right-click the component in the graphics area or the component's name in the FeatureManager design tree.
2. Select Fix or Float.

Make sure you see '(f)' as shown below for the parts that you fixed in the assembly.

Step 2: Setting up the Motor:

You can enable to view temporary axis, hide the components to reduce the complexity and choose the desired axis/face and direction to establish the motor.

The motor type chosen is the 'Rotary Motor' with an 'Constant Speed' of '200 rpm'.

Note that the components for Fixing and Rotation (i.e., providing the rotary motion by setting up the motor) will change from case to case.

Step 3: Setting up the Contacts:

The contacts will remain same for almost all the cases. We have used contact groups as shown below and material type is Steel (Dry).

Solid Body Contact1: Contact between the Sun Gear and all the four Planetary Gears.

Solid Body Contact2: Contact between the Ring Gear and all the four Planetary Gears.

Solid Body Contact3: Contact between the Carrier and all the four Planetary Gears.

Step 4: Adjusting the time for the Motion Analysis, Calculate and Run:

This adjustment to time is the one parameter which lets us decide how long the analysis is to be performed. This can be achieved by dragging the end key of the Rupesh_Final_Assem to the desired time on the timeline. Here, the Motion Analysis is done for the first 8 seconds. Once done, just hit the Calculate button and the Motion Analysis has successfully run.

Now we are ready to plot the results we want.

Note that the SOLIDWORKS Motion must remain enabled during this whole process.

Step 5: Plotting:

In this case, we have plotted the Angular Velocity of the Carrier with respect to time. The procedure is as shown.

The result plotted is as shown below.

Observations & Conclusions 1:

We can see that when the Ring Gear is fixed, the input at the centre axis of sun gear results in the output at the carrier.

The planet gear not only rotates about their axis but are also forced to roll on the inside of the ring gear since it is fixed.

For a constant speed of 200 rpm given to the Sun Gear, the Angular velocity of the carrier is approximately 278 degrees/second.

For a more clear understanding on how this motion is transmitted from the sun gear to the carrier, the following video has been shown at one fourth speed (x.25) of the original.

MOTION STUDY 2

Motion Study 2 refers to the Motion Analysis of the Planetary Gear Assembly (i.e., Rupesh_Final_Assem.SLDASM) for the Case 2.

	Fixed	Input	Output
Case 2	Sun Gear	Ring Gear	Carrier

To establish this study, copy 'Motion Study 1'. Change the Ring Gear back to float. Now fix the Sun Gear. Right-click on RotaryMotor2 to setup the input for the Ring gear. Select the centre axis of the ring gear as the reference and set up the direction of rotation. Calculate and Run the Motion Analysis.

Since the Angular Velocity was plotted with respect to time for the Carrier in Motion Study 1, which is same output in this case too, we simply need to click on 'Show Plot' after the calculations are done.

The result plotted is as shown below.

Observations & Conclusions 2:

We can see that when the Sun Gear is fixed, for the input given to the Ring Gear the output at the carrier is obtained.

Since the ring gear is bigger in diameter and planet gears are comparatively smaller in the diameter, the velocity achieved from the smaller gear is higher because the velocity ratio is high.

For a constant speed of 200 rpm given to the Ring Gear, the Angular velocity of the carrier is approximately 880 degrees/second.

For a clearer understanding on how this motion is transmitted from the ring gear to the carrier, the following video has been shown at one fourth speed (x.25) of the original.

MOTION STUDY 3

Motion Study 3 refers to the Motion Analysis of the Planetary Gear Assembly (i.e., Rupesh_Final_Assem.SLDASM) for the Case 3.

	Fixed	Input	Output
Case 3	Carrier	Sun Gear	Ring Gear

To establish this study, copy 'Motion Study 1'. Change all the components back to float. Now fix the Carrier. Input is already set for the Sun Gear. Calculate and Run the Motion Analysis.

The result plotted is as shown below.

Observations & Conclusions 3:

We can see that when the Carrier is fixed, for the input given to the Sun Gear the output at the Ring Gear is obtained.

The planet gears rotate only about their axis and transmit motion from sun to the ring. Since the ring gear is bigger in diameter and driven by a smaller gear i.e., the sun gear the angular velocity achieved is less.

For a constant speed of 200 rpm given to the Sun Gear, the Angular velocity of the carrier is approximately 350 degrees/second.

For a clearer understanding on how this motion is transmitted from the sun gear to the ring gear, the following video has been shown at one fourth speed (x.25) of the original.

Cited under: MBD