1

PROJECT REPORT

ON

“PLANETARY GEARBOX”

INDEX

S.

NO.

TITLE PAGE

NO.

1. INTRODUCTION

2. OBJECTIVES

3. PLANETARY GEAR RATIO

4. NOTABLE DESIGN POINTS

4.1 ADVANTAGES OF PLANETARY GEARS

4.4 NECESSITY OF TWO SPEED GEARBOX

5. POSSIBLE COMBINATIONS

5.1 FIXING SUN GEAR

5.2 FIXING CARRIER

5.3 FIXING RING

6. ACTUATION METHOD

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7. DESIGN CALCULATION’S

7.1 GEAR CALCULATION

7.2 HOLDING TORQUE ON RING GEAR

7.3 MAXIMUM NUMBER OF PLANETARY GEAR

7.4 DESIGN OF SHAFT

7.5 CHOICE OF BEARING

8. DESIGN IN SOLID WORKS

9. DESIGN IN ADAMS

11. CONCLUSION

12. REFERENCES

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INTRODUCTION

Planetary gear trains is an simple epicyclic gear train. Planetary gear set mainly consist of

four parts Sun, Carrier, Planet shown in Figure surrounded by planet gears. The outermost

gear, the ring gear (internal teeth spur gear), meshes with each of the planet gear. The planet

gears revolve around their own axis, Carrier that fixes the planet in orbit relative to each

other. Planetary gear is a widely used industrial product in mid-level precision industry, such

as printing lathe, automation assembly, semiconductor equipment, and automation system.

Planetary gear transmissions offer more options for generating transmissions ratios, more

compact, space and weight saving design, noise reduction, higher efficiency, more favourable

load distribution and higher load carrying capacity in comparison to conventional

transmissions. In planetary gear set the load transmitted is divided among the number of the

planet gear in the system. In planetary gear set different ratios can be obtained by keeping

any of the members of the planetary gear set fixed and also varying the input and output. By

compounding different result can be obtained as the output of planetary gear vary in different

situations, in planetary gear trains (shown in Figure (2)) different speeds can be obtained by

just governing one of the fixed member of the planetary gear set, in planetary gear if any

member is not fixed it act as a neutral condition no output is being obtained, similarly if any

two members are given same input the reduction is 1

To compare with traditional gearbox, planetary gear has several advantages. One advantage is

unique combination of both compactness and outstanding power transmission efficiencies. A

typical efficiency loss in planetary gearbox arrangement is only 3% per stage. This type of

efficiency ensures that a high proportion of the energy being input is transmitted through the

gearbox. Another advantage of the planetary gearbox arrangement is load distribution

because the load transmitted is shared between multiple planets, torque capability is greatly

increased. Greater load ability, as well as higher torque density is obtained with more planets

in the system. The planetary gearbox arrangement also creates greater stability due to the

even distribution of mass and increased rotational stiffness.

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Figure (1)

Figure (2)

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Spur Gear

To generate a spur gear, some terminologies of the gear should be taken into consideration.

The most important parameters in modelling we need to set the planetary gear are ---

numbers of tooth, module, pitch circle diameter, pressure angle, basis circle diameter,

addendum and dedendum.

Spur gear have two types of profile cycloidial and involute, Involute profile have some

advantages as it is easy to manufacture and The centre distance of spur gear can be varied

without changing the velocity ratio

Figure (3)

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Standard pressure angles are 14.5, 20, 25. Earlier gears with pressure angle 14.5 were

commonly used because the cosine is larger for a smaller angle, providing more power

transmission and less pressure on the bearing; however, teeth with smaller pressure angles are

weaker.

The gear with pressure angle 25 the contact ratio decreases and also the force of separating

gear from shaft increase.

We used pressure angle 20 degree for spur gear

FIGURE (4)

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GEAR RATIO OF PLANETARY GEAR

TABLE (1) – Gear ratio

Here,

TS = Number of teeth on sun gear

TR = Number of teeth on ring gear

NR = Number of revolutions on ring gear

NS = Number of revolutions on sum gear

NC = Number of revolutions on carrier

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Calculation of Gear ratio

METHOD 1

(NR / NS) = (TR / TS)

NR = (NS)*(TR / TS)

(NC / NS) = {TS / (TR + TS)}

(NC) = (NS)*{TS / (TR + TS)}

(NC / NR) = {TR / (TR + TS)}

(NC) = (NR)*{TR / (TR + TS)}

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METHOD 2

Serial No. Condition of motion Carrier Ring Sun

1 Carrier is fixed and ring

rotates through +1

revolutions

0 +1 - (TR / TS)

2 Carrier is fixed and ring

rotates through +X

revolutions

0 +X - X(TR / TS)

3 Add +Y revolutions to all

elements

+Y X + Y (Y - X)(TR/TS)

TABEL (2)

X+Y =NR

Y – X (TR / TS) = NS

NR – NS = X + Y – Y + X (TR / TS)

X = (NR - NS) / {1 + (TR / TS)}

Y = (NS) / {1 + (TR / TS)}

SITUATION (1)

RING = FIXED, CARRIER = OUTPUT, SUN = INPUT

NR= 0

X = (-NS) / {1 + (TR / TS)}

Y = (NS) / {1 + (TR / TS)}

OUTPUT ON CARRIER = Y

Y = NS TS / (TR + TS)

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Combinations in Planetary gears

Case

no.

SUN GEAR CARRIER RING GEAR SPEED TORQUE DIRECTION

1 INPUT OUTPUT FIXED Maximum

reduction

Increase Same as input

2 FIXED OUTPUT INPUT Minimum

reduction

Increase Same as input

3 OUTPUT INPUT FIXED Maximum

increase

Reduction Same as input

4 FIXED INPUT OUTPUT Minimum

increase

Reduction Same as input

5 INPUT FIXED OUTPUT Increase Increase Reverse of input

6 OUTPUT FIXED INPUT Reduction Reduction Reverse of input

7* When no member is held or locked no output is obtained, it results in neutral condition

8** When any two members are held together or given speed and direction same as input, direct drive

occurs i.e. reduction obtained is 1:1

TABLE (3)

Objective to be achieved

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A Two speed gearbox for a robotic platform is to be developed with output torques around

400 Nm and 100 Nm

Actuation method

Input = Sun

Output = Carrier

Governing = Ring

Case 1

Keeping ring gear fixed

1. By using Brake pads

2. By using Electromagnetic brakes

3. By using projection (like Dog Clutch) governed by Solenoid

Case 2

Running ring and sun gear at same speed

1. By using Friction Plate

2. By using Electromagnetic brakes

3. By using Projection ( Like Dog Clutch) governed by Solenoid

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Brake Pads

Brake pads are generally used in cars brake assembly. Brake pads are of two type, Semi

Metallic brake pads and Ceramic brake pads. Brake pads are efficient in braking but as

ceramic brake pads need warming up time to hold the object; it cannot be used because it will

take time to completely fix ring gear.

Semi metallic brake pads can be used in cooler regions but these brake pads create large

amount of noise.

Semi metallic brake pads produce dust particles at the time of braking

Brake pads require high maintenance cost

Wear and tear is very high in brake pads

Electromagnetic brakes

Electromagnetic brakes are widely used today for braking. In electromagnetic brakes when

the current is passed the it holds the shaft and brake is applied and vice versa when the

current is passed again the shaft starts to rotate

Electromagnetic brakes installation is difficult due to the length constraints; they require

more length as compared to any other braking mechanism that can be used.

Electromagnetic brakes are manufactured in standard sizes; the size required is not easily

available in market

Electromagnetic brakes gets heat up after working sometime, it requires an external cooling

mechanism to keep brakes cooler

Electromagnetic brakes require periodic maintenance

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Electromagnetic brakes do not work well in presence of grease or oil, Grease and oil will be

provided on the inner side of the gear box, it will be difficult to fit electromagnetic brakes in

there

Clutch plate

Clutch plates are also used in braking assemblies; in Clutch plate stationary plate is rubbed

against the rotating plate with some force so that due to friction it stops the moving plate.

Clutch plates are prone to heat failure

As the result of friction a large amount of heat is produced this can lead to clutch plate failure

An external cooling mechanism required to keep the clutch plates cool

Due to length constraints external cooling mechanism cannot be applied.

Dog clutch

Dog clutch is also used in braking mechanism, Dog clutch consist of a plate with external

teeth’s on it(Shown in figure()) and the plate in which it is to be engaged consist holes when

the plate with teeth is pushed towards the plate with holes, the teeth engage with holes and

restricts the plate to rotate further.

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Figure (10)

Solenoid

Solenoid is used to push or to bring back any mechanism d, it consist of a pin which holds the

mechanism to be pushed, solenoid works on battery when power is on the screw is pushed

outside or inside depending upon the assembly

Figure (11)

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Dog Clutch and Solenoid are used in this gearbox; the dog clutch mechanism is being

governed by the solenoid, Two plates with teeth will be used and the plate with holes will be

represented by the ring of the 1st planetary gear box. One plate will be on left side of the ring

gear and other will be on the right hand side and will be governed by solenoid

Maximum Number of Planet Gear in a Planetary Gear Set

Maximum number of planet gears in planetary gear set calculated by taking a limiting

condition of two planet gear meeting at point while revolving around the sun

Figure (12)

Calculation

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From Figure ()

L > 2(r2+h2)

Where

1. L = Length between two planet gears

2. r1 = Radius of sun gear

3. r2 = Radius of Planet gear

4. h2= Height of the teeth of planet gear

Schematic model

MotorInput Shaft

Output shaft

Solenoid

S

Ring

S

P

PP

P

S

P

P

R

R

C C

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Figure (13)

Design Explanation

Input from the motor is given directly to the sun gear (30 teeth) of the 1st planetary gear set.

The sun is surrounded by three planetary gears (30 teeth), planets are enclosed in ring gear

(90 teeth). The ring gear is the governing part of the 1st planetary gears set. Ring gear will be

kept fixed with the help of the projection having teeth; those teeth will engage with ring gear

and keep the ring gear fixed. To run the ring gear at the same speed as of sun another

projection is used, both the projection will be connected and governed through solenoid.

When the solenoid is on the projection on the right side of the ring gear keeping ring fix will

be pushed back and the projection on left side of the ring gear will be engaged. In this way

two speeds can be obtained, one by fixing the ring gear (case 2) and other by running the ring

gear at same input as of the sun gear (Case 8). In both the cases the input to the sun of the 2nd

planetary gear set will vary and hence output varies

Then the output from 1st planetary gear set taken from carrier is given to the sun gear of the

2nd planetary gear set. In both the cases the input to the sun of the 2nd planetary gear set will,

in 2nd planetary gear set the ring is kept fixed by bolting it with the casing.

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Similarly the output from the carrier of the 2nd planetary gear set will be given to the sun gear

of the 3rd planetary gear set and hence output can be obtained by the output shaft from the

carrier of the 3rd planetary gear set.

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Figure (14)

Solenoid and governing mechanism assembly

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Design Calculation

Pressure angle = 20 degrees

At 20 degree minimum number of teeth on the Gear is around 17

Derived by the equation

Z1 = (2 K1) / Sin2 (20) (K1 = 1 for 20 degree involute sub depth teeth)

Z1 = 17

Assumptions

1. Material used for gear = 17 Cr Ni Mo 6

2. Module =1

3. Safety factor on motor torque = 2

4. Safety factor on Hertizian fatigue limit of material = 1.25

5. Overall safety factor = 4.05

Limiting Conditions

1. The length of whole gearbox = 375mm (Including Motor)

2. Diameter of the gearbox not to exceed = 140mm

Material Properties (17 Cr Ni Mo 6)

1. Maximum Hertizian Fatigue Limit = 1200

2. Elasticity modulus = 210000 N/mm2

3. Poisson’s ratio = 0.3

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Gear Designed

Gear are designed with help of

SIS- Swedish Institute of Standards, 1978

(Svensk standard SS 1863 & SS 1871)

In this we assumed

1. Pressure angle

2. Safety factor on torque = 2

3. Required gear ratios

4. No. of teeth on sun gear

5. Material = 17 Cr Ni Mo 6

6. Safety factor for material hertizian fatigue = 1.25

7. As per required radius of ring gear

Elasticity Modulus S

Elasticity Modulus P

Poisson's Ratio S

Poisson's Ratio P

Material Factor Zm S&P

Contact Ratio S&P

Contact Factor S&P Khα Khβ

in Mpa (N/mm^2)

In Mpa (N/mm^2)

210000 210000 0.3 0.3 271.0279092 1.71353362 0.873015154 1 1.3210000 210000 0.3 0.3 271.0279092 1.65575579 0.88397666 1 1.3210000 210000 0.3 0.3 271.0279092 1.65575579 0.88397666 1 1.3

Pressure Angle Calculated

Torque Gear RatioTeeth on

Sun

Form Factor Zh (Sun & Planet)

Maximum Hertzian Fatigue

Safety Factor Hertzian Fatigue

Hertzian Fatigue Limit

α (degrees) N-mmin Mpa

(N/mm^2)

20 8000 4 40 1.763929606 1200 1.25 96020 32000 7 20 1.763929606 1200 1.25 96020 224000 7 20 1.763929606 1200 1.25 960

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(Rr)2 * b (Rr) (Rr)

2 b (width)

(hertzian pressure S&P)

1474.301236 60 3600 0.4095289673.958852 60 3600 2.68721167717.71196 60 3600 18.81048

By calculating required width for each planetary gear set, other required dimensions can be

calculated.

Sizes of other member of planetary gears can be calculated as

Radius of Sun gear + Diameter of planet gear = Radius of the ring gear

Radius of Carrier = Radius of sun gear + Radius of planet gear

Module = 1

S. No. Presssure angle No. of teeths on Sun gear (ZS) Expected gear ratio No. of teeth on Ring gear (ZR) Module (m)

20 30 4 90 120 20 7 121 120 20 7 121 1

rS rR rP rC

mm mm mm mm15 45 15 3010 60 25 3510 60 25 35

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By Conventional method

1. Calculation is verified with help of Indian standards

2. In this we assume

S. No. Presssure angle No. of teeths on Sun gear (ZS) Expected gear ratio No. of teeth on Ring gear (ZR) Module (m)

1 20 30 4 90 12 20 20 7 121 13 20 20 7 121 1

rS rR rP rC NS NC

mm mm mm mm 15 45 15 30 1600 40010 60 25 35 400 56.7375886510 60 25 35 56.73758865 8.047884915

VCo (Medium shocks

3 hrs/day) CV Torque

m\s Nm2.51232 1.25 0.548332351 80.41872 1.25 0.879286884 32

0.059392908 1.25 0.980898873 224

WT Y b Stress

N m N/m2

0.533333333 0.388104 0.01 200.49185173.2 0.340376 0.01 855.362960222.4 0.340376 0.02 2683.643629

By conventional method it is being checked that each designed gear is within required stress

limits

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Sizes of gear used in Gear box

1st Planetary gear set (Module =1)

Spur Gear (sun) = 30 teeth

Spur Gear (Planets) = 30 teeth

Spur gear with internal teeth (Ring) = 90 teeth

Outside Diameter of Ring gear = 120mm

2nd Planetary gear set (Module = 1)

Spur Gear (Sun) = 20 teeth

Spur Gear (Planets) = 50 teeth

Spur Gear with internal teeth (Ring) = 120 (After addendum modification taken as 121)

Outside Diameter of Ring gear = 141mm

3rd Planetary gear set (Module = 1)

Spur gear (sun) = 20 teeth

Spur gear (Planets) = 50 teeth

Spur gear with internal teeth (Ring) = 120 (After addendum modification taken as 121)

Outside Diameter of Ring = 141mm

Outside Diameter are selected as M6 bolts will be used in assembly to hold the ring gear

fixed i.e. 11mm extra space is provided for 6mm hole in the ring so that teeth of ring gear are

not damaged during drilling

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Holding Torque on Ring gear

Planetary gear set (1)

No. of teeth on sun gear = 30

No. of teeth on planets = 30

No. of teeth on ring gear = 90

Amount of torque on sun = 8 Nm

Holding torque on ring gear = (Amount of torque on Sun / Radius of sun gear) * (Radius of

Ring gear)

Holding torque on 1st ring gear = (8/30) * 90

= 24 Nm

Similarly

Planetary gear set (2) & planetary gear set (3)

No. of teeth on sun gear = 20

No. of teeth on planets = 50

No. of teeth on ring gear = 121

Holding torque on 2nd ring gear = (32/20)*121

= 193.6 Nm

Holding torque on 3rd ring gear = (224/20)*121

= 1355.2 Nm

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Design of Governing mechanism

Design of governing mechanism depends upon two parts

1. No. of teeth on the governing part

2. Probability of engagement

When the Vehicle is on an inclined plane and brake is applied, the motor stops giving input to

the sun of 1st planetary gear set but the output shaft have tendency to rotate and as the ring of

the 1st planetary gear set have tendency to rotate (shown in figure()) . Therefore the vehicle

moves backwards and then brake is applied. To reduce this no. of teeth on the governing part

are to be adjusted

Figure (15)

Ring gear have tendency to move anticlockwise

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(1/120) = (X/90)

X = 3/4

(1/7)*(1/7)*(3/4)

0.015

A C S

Ts TR

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Probability of engagement of governing mechanism

Probability of the engagement depends upon the angle teeth as the teeth will not engage

Figure (16)

Let ABCD be the teeth to engage and CDEF be the projection to stop the teeth to engage

Then if CD line have to engage then AB must cross EF therefore the total amount of the

angle travelled is twice the angle of the projection on ring gear.

Therefore

Angle of the teeth taken = 7 degree

No. of teeth = 3

Angle of not engaging = (14*3) = 42 degree

Therefore

Probability of engagement = {(360 – 42)} / (360)

= .88 or 88%

A

B

C

D E

F

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Design of shaft

In designing shaft on basis of strength following cases may be considered

1. Shaft subjected to twisting moment or toque only

2. Shaft subjected to bending moment only

3. Shaft subjected to combined twisting and bending moment

Shaft subjected to twisting moment only

Shaft rotating at 36 rpm

Torque applied on the shaft = 1568000 N mm

Material used for Shaft = EN24 (34 Cr Ni Mo 6)

Yield stress of EN24 = 680 N/mm2

Factor of safety = 2

Allowable Shear stress = (680 / 2)

= 340 N/mm2

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Design of key way of shaft

Key way of the shaft is designed on the basis of the diameter of the shaft

Diameter of shaft =

Width of key, W = H = (d/4)

W = H =

L = 1.5d

L=

Crushing

Crushing stress = (4TMAX / d H L)

L=

Shear

Stress = (2TMAX / d W L)

L =

31

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Conclusion

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References

Antony (2003)

Gerhard, Precision gearhead torque rating for automation and robots, Motion System Design, June 2003

Buckingham (1963)

Buckingham Earle, Analytical mechanics of gears, Dover Publications Inc. 1963

Crowder (1995)

Crowder, Richard M. Electric Drives and Their Controls, Oxford Science Publications ISBN 0 19 856565 8,

1995

Feinstein (1997)

Feinstein Alan, Bayside Motion Group, Power Transmission Design, 1997

Roos, Wikander (2004)

Roos Fredrik, Wikander Jan, Towards a design and Optimization Methodology for Automotive Mechatronics,

FISITA World Congress, Barcelona, May 2004

1. SS 1863

Svensk Standards SS 1863, kugg och snӓckvӓxlar – Cylindriska kugghjul med raka kuggar – Geometriska data,,

Spur gears- geometrical data, Utgӓva 4, SIS- Swedish Institute of Standards, 1978

2. SS 1871

Svensk Standards SS 1863, kugg och snӓckvӓxlar – Cylindriska kugghjul med raka eller –sneda kuggar –

Berӓkning av bӓrformaga. Spur and helical gears-Calculation of load capacity. Utgӓva 3, SIS- Swedish Institute

of Standards, 1978

Vedmar (2002)

Vedmar Lars, Markinelement, Lunds Tekniska Hogskola, 2002

3. Khurmi R.S. & J.K. Gupta, “Machine Design” by S. Chand Publications

4. PSG Design Data by PSG Publications

5. Gear Guide by KHK

6. Boston Gear Catalogue

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