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1. Design and Analysis of Gear Box for High
Power Transmission
Presented By
MOHD AMIR(13MEB122)
MIR MONIR ALAM (13MEB205)
MUZZAMMIL AHMAD(13MEB032)
1
Under the Supervision of
Prof. MD. Naushad Alam

2. Table of content
 Introduction
 Design of gears
 Design of shafts
 Design of keys
 Introduction to ABAQUS/CAE
 Future work
 References
2

3. Introduction
 Gearbox often referred as transmission unit that uses gears and gear trains to
provide speed and torque conversions from a rotating power source to another
device. Gearboxes are employed to convert input from a high speed power sources
to low speed(E.g. Lift, Cranes and Crushing Machine) or into a many of
speeds(Lathe, Milling Machine and Automobiles).
 A gearbox that converts a high speed input into a single output it is called a single
stage gearbox. It usually has two gears and shafts.
 A gearbox that converts a high speed input into a number of different speed
output it is called a multi-speed gear box. Multi speed gear box has more than two
gears and shafts. A multi speed gearbox reduces the speed in different stages.
3

4. Components of a Gear Box
 Gears :Toothed Mechanical component transmit power or change direction of
speed when engaged with another gear.
 Shafts :Circular cross section member supported on bearing to transmit power
by gears.
 Keys :Element used for joining transmission shaft to rotating member like
gears, pulleys, flywheels etc.
 Bearing: A bearing allows constrained relative motion between two or more
parts, typically rotation or linear movement
 Housing: Casing that surrounds the mechanical components of a gear box
provides lubrication, protection and mechanical support for the moving
components.
4

5. Gears
Classification of Gears
Gears are classified on the position of axis of shaft
 Parallel shaft: Spur gear, helical gear.
 Coplanar and intersecting shaft: Bevel gear.
 Non-intersecting and non-parallel shaft: Worm gear.
5

6. Helical Gears
 Helical Gear :These gears are usually thought of as high speed gears. Helical
gears can take higher loads than similarly sized spur gears. The motion of
helical gears is smoother and quieter than the motion of spur gear. Single
helical gears impose both radial loads and thrust loads on their bearings and
so require the use of thrust bearings. The angle of the helix on both the gear
and the must be same in magnitude but opposite in direction, i.e., a right
hand pinion meshes with a left hand gear.
6

7. TERMS USED IN GEAR
 Pitch surface: The surface of the imaginary rolling cylinder (cone, etc.) that
the toothed gear may be considered to replace.
 Pitch circle: A right section of the pitch surface.
 Addendum circle: A circle bounding the ends of the teeth, in a right section
of the gear.
 Root (or dedendum) circle: The circle bounding the spaces between the
teeth, in a right section of the gear.
 Addendum: The radial distance between the pitch circle and the addendum
circle.
 Dedendum: The radial distance between the pitch circle and the root circle.
 Clearance: The difference between the dedendum of one gear and the
addendum of the mating gear.
7

8. TERMS USED IN GEAR
 Tooth space: pitch diameter the distance between adjacent teeth measured
on the pitch circle.
 Backlash: The difference between the circle thickness of one gear and the
tooth space of the mating gear.
 Module (m): Pitch diameter divided by number of teeth. The pitch diameter
is usually specified in inches or millimetre; in the former case the module is
the inverse of diametral pitch.
 Line of action: A line normal to a pair of mating tooth profiles at their point
of contact.
 Path of contact: The path traced by the contact point of a pair of tooth
profiles.
8
𝑚 =
𝐷
𝑇

9. TERMS USED IN GEAR
 Pressure angle (α): The angle between the common normal at the point of
tooth contact and the common tangent to the pitch circles. It is also the
angle between the line of action and the common tangent.
 Base circle: An imaginary circle used in involute gearing to generate the
involutes that form the tooth profiles
9

10. Standard Tooth System For Gears
To reduce the varieties of gears to a manageable numbers, standards are
evolved. Standard makes it easy for design, production, quality assurance,
replacement etc. Three commonly used pressure angles are 14.5,20 and 25
pressure angle systems.one can have full depth gears or stronger stub tooth
gears. In Standard tooth system for metric gears, addendum: a =1m, dedendum:
b= 1.25m where as the for the stub tooth gears, addendum a = 0.8m and
dedendum: b= 1.0m. The shorter tooth makes it stronger and its load carrying
capacity increases. It also helps in avoiding interference in certain cases.
10

11. Gear Assembly
11

12. Gearbox Specification
Motor used DC Motor
Power transmitted 55 kW
Speed variation 1600-200 rpm
Distances between shafts 1 & 2 244 mm
Distances between shafts 2 & 3 266 mm
12

13. Design of Gear
Power being transferred = 55 kW
Speed at the input shaft = 1600 rpm
Gear ratio for the first gear set = 4:1
Let number of teeth on pinion = 18
(The min. of teeth in the pinion to avoid undercutting should not be less than 17)
Taking standard pressure angle φ = 200
Taking normal module (mn) = 5 mm
Say centre distance being, cd
Then Helix angle is given by,
𝜓 = cos−1
(
𝑚 𝑛(𝑇1 + 𝑇2
2 ∗ 𝑐𝑑
13

14. Calculation Continued
Now, transverse module,
Pitch dia. Of the pinion
Contact point velocity V is given by,
𝑚 𝑡 =
𝑚 𝑛
cos(𝜓
𝜑 𝑡 = tan−1
(
tan(𝜑
tan(𝜓
𝑑1 =
𝑚 𝑛 ∗ 𝑇2
cos(𝜓
𝑉 =
𝜋𝑑1 𝑁
60000
14

15. Calculation Continued
If P be the power transmitted then
Tangential force component is given by:
Other force component
Torque transmitted is calculated by:
𝐹𝑡 =
𝑃
𝑉
𝐹𝑟 = 𝐹𝑡tan(𝜑 𝑡 𝐹𝑎 = 𝐹𝑡tan(𝜓
𝐹𝑛𝑒𝑡 =
𝐹𝑡
cos(𝜑 cos(𝜓
𝑇𝑂𝑅𝑄𝑈𝐸 =
𝑃
𝜔
15

16. Bending Analysis
Various factors have to be incorporated to account for various practical
complications.
Velocity factor (For helical gears):
Other factors incorporated are geometry Lewis form factor Y in bending And
material Ultimate Tensile Strength being UTS and Yield Strength
For the selected material, alloy steel C45
UTS = 686 MPa
YTS = 353 MPa
𝐾 𝑉 =
78
78 + 200𝑉
16

17. Calculation Continued
Say, FOS in permissible yield strength is 3.5
Then, Spermissible = (YTS/3.5)
Face width is given by
Bending stress developed by:
Fatigue strength is given by:
𝐵 =
𝐹𝑡
𝐾 𝑉 ∗ 𝑚 𝑡 ∗ 𝑌 ∗ 𝑆 𝑝𝑒𝑟𝑚𝑖𝑠𝑠𝑖𝑏𝑙𝑒
𝑆 𝑏 =
𝐹𝑡
𝐾 𝑉 ∗ 𝐵 ∗ 𝑚 𝑡 ∗ 𝑌
𝑆𝑒 = 𝐾 𝑎 ∗ 𝐾𝑏 ∗ 𝐾𝑐 ∗ 𝐾 𝑑 ∗ 𝐾𝑒 ∗ 𝐾𝑓 ∗ 𝑆𝑒𝑛𝑑𝑢𝑟𝑎𝑛𝑐𝑒
17

18. Results
Gear 1
Gear 2
Material UTS
(MPa)
YTS
(MPa)
B
(mm)
Sb
(MPa)
Se
(MPa)
𝜓
(rad)
FOS
C-35 539 305 56 56 270 0.397 4.82
C-45 686 353 52 65 369 0.397 5.67
C-50 735 372 49 67 422 0.397 6.29
Material UTS
(MPa)
YTS
(MPa)
B
(mm)
Sb
(MPa)
Se
(MPa)
𝜓
(rad)
FOS
C-35 539 305 43 67 219 0.397 3.26
C-45 686 353 37 77 259 0.397 3.36
C-50 735 372 35 81 289 0.397 3.56
18

19. Result Table for Gear
Gear 3
Gear 4
Material UTS
(MPa)
YTS
(MPa)
B
(mm)
Sb
(MPa)
Se
(MPa)
𝜓
(rad)
FOS
C-35 539 305 98 62 219 0.311 3.53
C-45 686 353 85 72 259 0.311 3.59
C-50 735 372 80 76 289 0.311 3.80
Material UTS
(MPa)
YTS
(MPa)
B
(mm)
Sb
(MPa)
Se
(MPa)
𝜓
(rad)
FOS
C-35 539 305 85 66 219 0.311 3.32
C-45 686 353 74 76 258 0.311 3.39
C-50 735 372 70 80 289 0.311 3.62
19

20. Forces on Gears
FORCE TABLE
Gear Drive Pitch diameter
in mm
Distancebetween
centre(mm)
TangentialloadWt
(N)
RadialLoad
Wr(N)
AxialloadWa
(N)
Resultantload
(N)
Speed
(m/s)
Torque
(N-m)
Pinion
(DP)
Gear
(DG)
Set 1 97.59 390 244 6730 2655 2823 7766 8.190 328.39
Set 2 173 346 260 15158 5794 4877 16945 3.385 982.77
20

21. Design of Shafts
Shaft is a circular cross section member supported on bearings for transmitting
power from one end to another end. During transmission of power shafts are
subjected to torsion and bending moment.
For designing shafts generally these two methods are adapted :-
 Design based on strength.
 Design based on Stiffness
ASME Design Code
ASME design code consider sudden and gradual load acting on shaft. (Shafts are
smaller in length so there is small angular deflection so while designing the
shaft only failure due to equivalent moments is considered.)
𝜏 𝑎𝑙𝑙𝑜𝑤𝑎𝑏𝑙𝑒 =
16
𝜋𝑑0
3 𝐾𝑏 𝑀 2 + 𝐾𝑏 𝑇 2
21

22. SHAFTS
22

23. BENDING MOMENT DIAGRAM for SHAFT:1
23

24. BENDING MOMENT DIAGRAM for SHAFT:2
24

25. BENDING MOMENT DIAGRAM for SHAFT:3
25

26. RESULT of SHAFTS
Result table for Shaft :1
Result for Shaft : 2
Bearing
No.
Ry
(N)
Rz
(N)
Max Bending
Moment
Horizontal
(mm)
Max Bending
Moment
Vertical
(mm)
Shaft
Position
at Max BM
(mm)
Torque
(Nm)
Dia.
(mm)
1 1864 5906 133.947 294.437 323.47 328.39 35.10
2 791 1649
Bearing
No.
Ry
(N)
Rz
(N)
Max Bending
Moment
Horizontal
(mm)
Max Bending
Moment
Vertical
(mm)
Shaft
Position
at Max BM
(mm)
Torque
(Nm)
Dia.
(mm)
3 10308 -3994 708.02 621.1 941.83 982.77 50.44
4 -7167 12422
26

27. RESULTS CONTINUED
Bearing
No.
Ry
(N)
Rz
(N)
Max Bending
Moment
Horizontal
(mm)
Max Bending
Moment
Vertical
(mm)
Shaft
Position
at Max BM
(mm)
Torque
(Nm)
Dia.
(mm)
5 -1385 7179 991.76 663.162 1193.05 982.77 52.6
6 -3790 18948
Result for Shaft :3
27

28. Design of Key
Key is a machine element which is used to connect the transmission shaft to
rotating machine elements like pulley, gear, sprocket or flywheel. Keys provide a
positive means of transmitting torque between shaft and hub of the mating
element. A slot is machined in the shaft or in the hub or both to accommodate
the key is called keyway. Keyway reduces the strength of the shaft as it results in
stress concentration.
TYPES OF KEYS
The following types of keys are important from subject point of view
 Sunk keys,
 Saddle keys,
 Tangent keys,
 Round keys, and
 Kennedy key.
28

29. Kennedy Key
The analysis of Kennedy key is similar to that of flat key. It is based on two
criteria failure either due to shear stresses or failure due to compressive
stresses. The forces acting on one of the Kennedy keys are shown in figure. Since
there are two keys, the torque transmitted by each key is half of the total
torque. The two equal and opposite forces P are due to transmitted torque. The
exact location of forces are unknown, it is assumed to act tangential to the shaft
diameter.
29

30. Calculation of Keys
Failure in a key may occur due to following two factors
 Failure due to shear stress,
 Failure due to crushing stress.
Shear stress is given by
And Crushing stress is given by
30
𝜎𝑠 =
𝑀𝑡
2 ∗ 𝑏 ∗ 𝑑 ∗ 𝑙
𝜎 𝑑 =
2 ∗ 𝑀𝑡
𝑏 ∗ 𝑑 ∗ 𝑙

31. Calculation of Keys
CALCULATION FOR KEY FOR GEAR A
Shaft diameter = 35mm
Now d = b = (Dia / 4)
Torque transmitted = 328.29 Nm
Key material is chosen C50 for which:
According to distortion energy theory
So,
Taking factor of safety of 3
31
𝜎𝑠 = 0.577𝜎 𝑦𝑡
𝜎 𝑑 =
𝜎𝑠
𝑓𝑜𝑠

32. Calculation of Keys Continued
Length of key according to shear criteria
Now we will check for crushing failure
32
𝑙 =
𝑀𝑡
2 ∗ 𝑏 ∗ 𝑑 ∗ 𝜎 𝑑
𝑙 =
2 ∗ 𝑀𝑡
𝑏 ∗ 𝑑 ∗ 𝜎𝑐

33. Calculation Result for Key
Gear Material Key Size
Code YTS
(MPa)
D
(mm)
B
(mm)
L
(mm)
A C50 375 9 9 43
B C50 375 13 13 22
C C65 460 13 13 68
D C65 460 14 14 62
33

34. Analysis in ABAQUS/CAE
 ABAQUS CAE provides a complete modeling and visualization environment for
ABAQUS analysis products. With direct access to CAD models, advanced
meshing and visualization, and with an exclusive view towards ABAQUS
analysis products, ABAQUS/CAE is the modeling environment of choice for
many ABAQUS users.
 Building input files by hand for large or complex models are too difficult.
 Build most models very quickly
 Gives a method to import models created by other software packages.
34

35. ABAQUS CAE modules
 Part – Create individual parts
 Property – Create and assign material properties
 Assembly – Create and place all parts instances
 Step – Define all analysis steps and the results you want
 Interaction – Define any contact information
 Load- Define and place all loads and boundary conditions
 Mesh – Define your nodes and elements
 Job – Submit your job for analysis
 Visualization- View your results
35

36. Part Module
 Create a new part as
 2-D planar, 3-D, Axisymmetric
 Type : Deformable, Discrete rigid, Analytical rigid, Eulerian
 Basic feature: shell, solid, shell, wire, point
 Approximate size:
 Used to create the material properties that will use in the simulation. It is
necessary to create a section and assign the section to the part.
 General properties like density,
 mechanical properties like elasticity, plasticity, viscosity, damping, etc.
Property Module
36

37. Assembly Module
 Used to instance several parts in the same assembly but in case of single part
it still has to be in an assembly. Then meshing is possible on the part or the
assembly.
 Create the simulation steps required for simulation.
 Add a step after the system created Initial step called Load Step.
 The procedure type is General and the type is Static.
 For the output stresses, strains, displacements, forces/reaction.
Step Module
37

38. Interaction Module
 Used to create interactions between parts or between a property and a part.
 The order in which the two surfaces are specified on the *CONTACT PAIR
option is critical because of the manner in which surface interactions are
discretized. For each node on the first surface (the “slave” surface)
ABAQUS/Standard attempts to find the closest point on the second surface
(the “master” surface) of the contact pair where the master surface's normal
passes through the node on the slave surface. The interaction is then
discretized between the point on the master surface and the slave node.
38

39. Load Module
 Used to create loads, boundary conditions, and predefined fields (like initial
temperature).
 This module is for creating finite element meshes.
 When choosing which parts mesh controls, element type, seed and mesh
instance hold down the Shift key and choose both parts.
Mesh Module
39

40. Job Module
 Create a job for analysis.
 Once this has been created submit the job for analysis.
 After completion of analysis results can be seen.
 Used after analysis to see different output variation like stresses, deflection,
temperature etc.
Visualization Module
40

41. Beam Created in ABAQUS/CAE
41

42. Meshing of the beam
42

43. Deflection variation
43

44. Shear stress distribution
44

45. Future work
 Surface wear Analysis of Gear
 Selection of bearing and Housing of gearbox
 Stress analysis of Helical Gear by Finite Element method with the help of
ABAQUS/CAE.
45

46. References
 Shigley, Joseph Edward, “Mechanical Engineering Design” (2nd Edition), Mc
Graw-Hill, New York, 1986.
 Bhandari, V.B., “Design of Machine Elements”, (3rd Edition, 15th Reprint), Mc
Graw Hill Education (India) Pvt Ltd, 2010.
 Khurmi, R.S. and Gupta, J.K. ”A Textbook of Machine Design”, (14th Edition),
Eurasia Publishing House (Pvt) Ltd., New Delhi, 2005.
 Bending Moment and Shear Force Diagram Calculator [see:
http://bendingmomentdiagram.com/free-calculator/-26/12/2016]
46

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