You are on page 1of 6

The Analysis and modification of spur gear design

Rajendra kumar patre, 2Tukesh kumar patel, 3Shankar dayal patel

Student, Bachelor of Engineering, Mechanical Engineering


Prakash Kumar Sen, 2Shailendra Kumar Bohidar

Faculty, Department of Mechanical Engineering


specific character, specific materials,with consideration of analysis of force,and its mechanical properties.these approach for morden
spur gear design developing the tooth profils with modified the shape and improving the diamention. The main purpose of morden sper
gear design it increases the power transmitting capacity and also improves the efficiency of power transmission.


This gearcan be meshed together correctly only if they

are fitted to parallel safts. The main reason for the popularity of
spur gear is their simplicity in design and manufacturing.the two
parameter i.e.tip radius and in tooth widths which play a key
role gear design are studied. [1]
A gear is a rotating machine part having cut
teeth.which is meshing the gear teeth to transmit the torque. A
geared device can be change the speed,direction of power
sources and magnitude.[2] The tooth meshing on another gear of
non roteting parts is called rack.when it a rotation it provide
transmission in analogous to the wheels in pully.It is the
cylindrical shaped its teeth are parallel in axis.its wide range of
application most commonly used.[3]

Fig.(a) pitch diameter fig.(b) pitch circle

Some important difination parameter

Design of spur gear:
In order to design, build and discuss gear drive systems
it isnecessary to understand the terminology and concepts
associated with gear systems.
Diametral pitch (DP):
The gear tooth size is described by diametral
Pitch larger gear have fewer teeth per inch of daimetral pitch,
daimetral pitch is inversely gear teeth size.

Pitch diameter:
The pitch diameter is indicatedthe diameter of
the pitch circle.if the diameter of the gear pitch is known pitch
diameter. We can mathamaticaly expression;

Pitch diameter (D): the diameter of the pitch circle from

which the gear is designe. An imaginary circle, which will
contact the pitch circle of another gear when in mesh.
Diametral pitch (P): a ratio of the number of teeth per inch of
pitch dimeter
Addendum (A): the radial distance from the pitch circle to the
top of the gear tooth

Dedendum (B): the radial distance from the pitch circle to the
bottom of the tooth
PD=pitch diameter
N= number of teeth on the gear
P=diametral pitch (gear size)

Outer diameter (OD): the overall diameter of the gear
OD= (N+2)/P
Root diameter (RD): the diameter at the bottom of the tooth
RD= (N-2)/P

Pitch circle:
The pitch circle is the is a
imaginary circle through contact the circle of two pitch of the
gear.the center of pitch circle meshing by center to center

Base circle (BC): the circle used to from the involute section of
the gear tooth
Circle pitch (CP): the measured distance along the
circumference of the pitch diameter from the point of one tooth
to the corresponding point on an adjacent tooth.

Circuler thickness (T): thickness of a tooth measure along the

circumference of the pitch circle
Clearance (C): refer to the radial distance between the top and
bottom of gears in mesh some mechanism,. In other word the
gap between two distances is known as clearance
Whole depth (WD): the distance from the top of the tooth to the
bottom of the tooth.the whole defth is calculated by
WD =2.157/P
Pressure angle (PA): it refers to the angle through which forces
are transmitted between meshing gears.
Center distance: the distance from the center shaft of one spur
gear to the center shaft of the other spur is called center
Gear ratio: the ratio of a given pair of spur gears is calculated
by dividing the number of teeth on the driven gear, by the
number of teeth on the drive gear [4].
Fig (c) Gear rotion= driven gear teeth/drive gear teeth

E1: gear longitudinal elastic modulus

E2: pinion longitudinal modulus
: Aallowable compressive stress [8]

Many gear solution could be left out of

consideration if a traditional approach based on a predetermined
set of rack diamention is applied.for example, spur gears with a
high operating pressure angle, or with a high contact ratiocould
not be produced with standard rack diamensions.
Figure 6a and 6b show these gears. Figures 6c and 6d are the
gear that are achievable using a standard generating rack that
D(w=15.9 ,=1.64).
The design intent of asymmetric teeth is to
improve performance of main contacting profiles by degrading
opposite profiles. These opposite profiles are unloaded or lightly
loaded, and usually work for a relatively short period. The
improved performance could mean increasing load capacity or
reducing weight, noise, vibration, etc.
Direct gear design for asymmetric tooth
profiles opens additional reservers for improvement of gear
drives with unidirectional load cycles that are typical for many
mechanical transmissions[4].[5]

Gear strength:
it has good strength,durability,wear resistance,
and chemical resistance,so can be used to each gear.gear wreck
will happen because of its tooth fatigue and tooth surface wear,
so strength design from both side is necessary.

Tooth surface strength:

Damage phenomenon like pitching and wear
will occur on tooth surface, and hertz formula (2) is generally
employed. W=2-bd1
(Sin2/2.8)(2Z2/ Z1+ Z2)(1/ E2 + 1/ E2)

W: pitch circumferential tangent load

B: face width
d1: gear pitch circle diameter
: meshing pressure
Z1: gear teeth number
Z2: pinion teeth number

is an

Assumptions made in the derivation are


The full load is applied to the tip of a single tooth

instatic condition


The radial component is negligible


The load is distributed uniformly across the full face



Forces due to tooth sliding frictionare negligible


Stress concentration in the tooth fillet is negligible

alternative approach to traditional gear design .it allows analysis

of a wide range of parameter for all possible gear combinations
in order to find the most suitable solution for a particular
application. This optimum gear solution cans exeed the limits of
traditional rack generating methods of gear design. [5]
If a gear does not produce a satisfactory
desgin based on bending requirements, a design alteration may
be needed. This is not always straightforward, since such
alterations may help in one area and hurt in another, and may
affect associated machine elements such as bearings. However,
some factors that improve bending performance are the

Reduction in the load, such as by increasing contact

ratio, or altering other aspects of the system.


Increase the center distance.


Apply gears with a finer pitch.


Use a higher pressure angle.


Usea helical gear instead of a spur gear.


Use a carburized material.


Increase the surface hardness by material selection, or

by performing a surface hardening operation.[6]


Improve the gear accuracy through manufacturing

process selection.


Use a wider effective face width.

10. Increase the lubricant film thickness.[6]

Fig (D) Gear toothascantilever beam [7]

Shows clearly that the gear tooth is stronger through out than
the inscribed constant strength parabola, except for the section at
a where parabola and tooth profile are tangential toeach other.

At point an ending stress is

= Mc/l =6Ft h/bt2

By similar triangles,

The Tooth stress for spur gear

Lewis considered gear tooth as a cantilever beam with static
normal force F applied at the tip

Substituting of Eqn
= 6Ft/4bx

Y = 2x/3p

spur gear with asymmetric teeth Mechanism and

machiny thory 2000.Issue 35.pp.117-130

Where y is defined as the Lewis from factor and

substituting eqn we get
= Ft/bpy


Litvion F.L. Q.Lain and A.L. Kapelevich ,asymmetric

modified gear drive reduction of noise Localization of
contact simulation of meshing and stress analysis,
coputer method in applied Mechanics and Engineering
2000 Issue 188.pp 363-390


CRC Fundamental of machine elements 3 rd schmid

Hamrock and Jacobson 2014 CRC pre,Desigan
procedure method to Increase the pitting Resistance


Figure shown in gear tooth scntilever

(prof.k.gopinath and prof.M.M.Mayuram)


Prof. K. Gopinath & Prof. M.M.M. Mayuram. (Indian

institute of technology) Spur gear lewis equation for
tooth bending stress

Eqn. is the basic Lewis equationin terms of circular pitch.

In SI units gears are more often made to standard modules.
Hence by substituting

m in Eqn we get

= Ft/ bym
Let y = y, which is known as modified Lewis from factor,
= Ft/ bym
Eqn. is the standard Lewis equation fortooth bending stress
based on module.
Both Y and y are functoions of tooth shape (but not size)
and therefore vary with the number of teeth in the gear.
These values can be olained.[8]



Sandeep, R.K. Suresh, B. jayachandraiah, Department

of Mechanical engg. Kalahasteeswara institute of
technology Srikala hasti chittor AP. Hydrabad India. De
Formabie body daynamic analysis of planetary gear
with thin rims-journal of sound and vibration262


B venkatesh, V. Kamala, A.M.K. Prasad Assoc. prof.

MED Vardhaman college of Engg, Hyderabad, India,
Professor. MED MJCET Hyderabad; DGM (Retd),
Hyderabad, India. Professer & Head
MED Osmania collage at engg. University, Hydrabad
India.Design, Modelling and Manufacturing of Helical


Gear ealction system LLC 105 Webster st Hanpover

Massachusetts 02339.


Kapelevich A.L. Geometry and desigan of involute