toothed wheels
Content
1
PROJECT REPORT
ON
“PLANETARY GEARBOX”
INDEX
S.
TITLE
NO
NO .
.
1.
INTRODUCTION
2.
OBJECTIVES
3.
PLANETARY GEAR RATIO
4.
NOTABLE DESIGN POINTS
4.1 ADVANTAGES OF PLANETARY GEARS
4.4 N ECESSITY OF TWO SPEED GEARBOX
5.
PAGE
POSSIBLE COMBINATIONS
5.1 F IXING SUN GEAR
5.2 F IXING CARRIER
6.
5.3 F IXING RING
ACTUATION METHOD
7.
DESIGN CALCULATION’S
7.1 G EAR CALCULATION
7.2 H OLDING TORQUE ON RING GEAR
7.3 M AXIMUM NUMBER OF PLANETARY GEAR
7.4 DESIGN OF SHAFT
7.5 CHOICE OF BEARING
2
8.
DESIGN IN SOLID WORKS
9.
DESIGN IN ADAMS
11.
CONCLUSION
12.
REFERENCES
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
3
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.
4
Figure (1)
Figure (2)
5
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)
6
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)
GEAR RATIO OF PLANETARY GEAR
7
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
8
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)}
9
(NC) = (NR)*{TR / (TR + TS)}
METHOD 2
Serial No.
Condition of motion
Carrier
Ring
Sun
1
Carrier is fixed and ring
0
+1
- (TR / TS)
0
+X
- X(TR / TS)
+Y
X+Y
(Y - X)(TR/TS)
rotates through +1
revolutions
2
Carrier is fixed and ring
rotates through +X
3
revolutions
Add +Y revolutions to all
elements
TABEL (2)
X+Y =NR
Y – X (TR / TS) = N S
NR – NS = X + Y – Y + X (TR / TS)
X = (NR - NS) / {1 + (T R / TS)}
Y = (N S) / {1 + (T R / TS)}
SITUATION (1)
RING = FIXED, CARRIER = O UTPUT , SUN = INPUT
NR= 0
X = (-NS) / {1 + (T R / TS)}
Y = (N S) / {1 + (T R / TS)}
OUTPUT ON CARRIER = Y
10
Y = NS TS / (TR + TS)
Combinations in Planetary gears
Case
SUN GEAR
CARRIER
RING GEAR
SPEED
TORQUE
DIRECTI
1
INPUT
OUTPUT
FIXED
Maximum
Increase
Same as in
2
FIXED
OUTPUT
INPUT
reduction
Minimum
Increase
Same as in
FIXED
reduction
Maximum
Reduction
Same as in
Reduction
Same as in
no.
3
OUTPUT
INPUT
4
FIXED
INPUT
OUTPUT
increase
Minimum
5
INPUT
FIXED
OUTPUT
increase
Increase
Increase
Reverse of
6
OUTPUT
FIXED
INPUT
Reduction
Reduction
Reverse of
7*
8**
When no member is held or locked no output is obtained, it results in neutral condition
When any two members are held together or given speed and direction same as input, direct dri
occurs i.e. reduction obtained is 1:1
TABLE (3)
Objective to be achieved
11
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
12
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
13
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.
14
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)
15
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
16
From Figure ()
L > 2(r2+h2)
Where
1.
2.
3.
4.
L = Length between two planet gears
r1 = Radius of sun gear
r2 = Radius of Planet gear
h2= Height of the teeth of planet gear
Schematic model
Ring
Solenoid
R
P
P
S
Motor
Input
Shaft
C
P
C
S
S
P
P
R
P
Outpu
t
shaft
17
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.
18
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.
19
20
Figure (14)
Solenoid and governing mechanism assembly
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.
2.
3.
4.
5.
Material used for gear = 17 Cr Ni Mo 6
Module =1
Safety factor on motor torque = 2
Safety factor on Hertizian fatigue limit of material = 1.25
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
21
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.
2.
3.
4.
5.
6.
7.
Pressure angle
Safety factor on torque = 2
Required gear ratios
No. of teeth on sun gear
Material = 17 Cr Ni Mo 6
Safety factor for material hertizian fatigue = 1.25
As per required radius of ring gear
22
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
23
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
By Conventional method
1. Calculation is verified with help of Indian standards
2. In this we assume
24
By conventional method it is being checked that each designed gear is within required stress
limits
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
25
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
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
26
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
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
27
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
A
C
Ts
(1/120) = (X/90)
X = 3/4
S
TR
28
(1/7)*(1/7)*(3/4)
0.015
Probability of engagement of governing mechanism
Probability of the engagement depends upon the angle teeth as the teeth will not engage
29
D
B
A
E
C
F
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%
Design of shaft
30
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
Design of key way of shaft
31
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=
32
33
Conclusion
34
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
35
PROJECT REPORT
ON
“PLANETARY GEARBOX”
INDEX
S.
TITLE
NO
NO .
.
1.
INTRODUCTION
2.
OBJECTIVES
3.
PLANETARY GEAR RATIO
4.
NOTABLE DESIGN POINTS
4.1 ADVANTAGES OF PLANETARY GEARS
4.4 N ECESSITY OF TWO SPEED GEARBOX
5.
PAGE
POSSIBLE COMBINATIONS
5.1 F IXING SUN GEAR
5.2 F IXING CARRIER
6.
5.3 F IXING RING
ACTUATION METHOD
7.
DESIGN CALCULATION’S
7.1 G EAR CALCULATION
7.2 H OLDING TORQUE ON RING GEAR
7.3 M AXIMUM NUMBER OF PLANETARY GEAR
7.4 DESIGN OF SHAFT
7.5 CHOICE OF BEARING
2
8.
DESIGN IN SOLID WORKS
9.
DESIGN IN ADAMS
11.
CONCLUSION
12.
REFERENCES
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
3
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.
4
Figure (1)
Figure (2)
5
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)
6
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)
GEAR RATIO OF PLANETARY GEAR
7
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
8
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)}
9
(NC) = (NR)*{TR / (TR + TS)}
METHOD 2
Serial No.
Condition of motion
Carrier
Ring
Sun
1
Carrier is fixed and ring
0
+1
- (TR / TS)
0
+X
- X(TR / TS)
+Y
X+Y
(Y - X)(TR/TS)
rotates through +1
revolutions
2
Carrier is fixed and ring
rotates through +X
3
revolutions
Add +Y revolutions to all
elements
TABEL (2)
X+Y =NR
Y – X (TR / TS) = N S
NR – NS = X + Y – Y + X (TR / TS)
X = (NR - NS) / {1 + (T R / TS)}
Y = (N S) / {1 + (T R / TS)}
SITUATION (1)
RING = FIXED, CARRIER = O UTPUT , SUN = INPUT
NR= 0
X = (-NS) / {1 + (T R / TS)}
Y = (N S) / {1 + (T R / TS)}
OUTPUT ON CARRIER = Y
10
Y = NS TS / (TR + TS)
Combinations in Planetary gears
Case
SUN GEAR
CARRIER
RING GEAR
SPEED
TORQUE
DIRECTI
1
INPUT
OUTPUT
FIXED
Maximum
Increase
Same as in
2
FIXED
OUTPUT
INPUT
reduction
Minimum
Increase
Same as in
FIXED
reduction
Maximum
Reduction
Same as in
Reduction
Same as in
no.
3
OUTPUT
INPUT
4
FIXED
INPUT
OUTPUT
increase
Minimum
5
INPUT
FIXED
OUTPUT
increase
Increase
Increase
Reverse of
6
OUTPUT
FIXED
INPUT
Reduction
Reduction
Reverse of
7*
8**
When no member is held or locked no output is obtained, it results in neutral condition
When any two members are held together or given speed and direction same as input, direct dri
occurs i.e. reduction obtained is 1:1
TABLE (3)
Objective to be achieved
11
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
12
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
13
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.
14
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)
15
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
16
From Figure ()
L > 2(r2+h2)
Where
1.
2.
3.
4.
L = Length between two planet gears
r1 = Radius of sun gear
r2 = Radius of Planet gear
h2= Height of the teeth of planet gear
Schematic model
Ring
Solenoid
R
P
P
S
Motor
Input
Shaft
C
P
C
S
S
P
P
R
P
Outpu
t
shaft
17
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.
18
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.
19
20
Figure (14)
Solenoid and governing mechanism assembly
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.
2.
3.
4.
5.
Material used for gear = 17 Cr Ni Mo 6
Module =1
Safety factor on motor torque = 2
Safety factor on Hertizian fatigue limit of material = 1.25
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
21
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.
2.
3.
4.
5.
6.
7.
Pressure angle
Safety factor on torque = 2
Required gear ratios
No. of teeth on sun gear
Material = 17 Cr Ni Mo 6
Safety factor for material hertizian fatigue = 1.25
As per required radius of ring gear
22
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
23
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
By Conventional method
1. Calculation is verified with help of Indian standards
2. In this we assume
24
By conventional method it is being checked that each designed gear is within required stress
limits
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
25
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
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
26
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
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
27
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
A
C
Ts
(1/120) = (X/90)
X = 3/4
S
TR
28
(1/7)*(1/7)*(3/4)
0.015
Probability of engagement of governing mechanism
Probability of the engagement depends upon the angle teeth as the teeth will not engage
29
D
B
A
E
C
F
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%
Design of shaft
30
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
Design of key way of shaft
31
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=
32
33
Conclusion
34
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
35
