Design and analysis of Gear Shaft - SSRG-Journalsinternationaljournalssrg.org/IJME/2015/Volume2-Issue9/IJME-V2I9P... · Design and analysis of Gear Shaft ... mechanical advantage

SSRG International Journal of Mechanical Engineering (SSRG-IJME) – volume 2 Issue 9 – September 2015

ISSN: 2348 – 8360 www.internationaljournalssrg.org Page 52

Design and analysis of Gear Shaft SingiReddy Ravinder

#1, Ramesh Banothu

*2

#1 M.Tech student, Mechanical, Vathsalya Institute of Science and Technology, Nalgonda Dist, Telangana, India *2 HoD, Mechanical, Vathsalya Institute of Science and Technology, Nalgonda Dist, Telangana, India

Abstract.A reduction gear box is part of a mechanical

system of gears and shafts used to reduce the rotational

speed of the input shaft to a slower rotational speed of the

output shaft. This reduction in output speed helps to

increase the torque of a system. Reduction gears are widely

used in power transmission devices to reduce the high

rotational speeds. Gears have wide variety of applications.

Gears are the most important component in power

transmission system. The gears generally fail when tooth

stress exceed the safe limit. It is essential to determine the

maximum stress that a gear tooth is subjected to, under a

specified loading. To prevent from failure Analysis is

carried on gears. In this study, visualize the forces, torques,

and bending moments that are created in the shaft during

operation. In the process of transmitting power at a given

rotational speed, the shaft is inherently subjected to a

torsional moment, or torque. Thus, torsional shear stress is

developed in the shaft. Finite element analysis was

performed to obtain the variation of the stress magnitude at

critical locations. Three dimensional model of the gear

shaft was created in Pro-E software. The load was then

applied to the FE model and boundary conditions were

applied as per the mounting conditions of the engine in the

ANSYS. .Also, a shaft usually carries power-transmitting

components, such as gears, belt sheaves, or chain

sprockets, which exert forces on the shaft in the transverse

direction (perpendicular to its axis). These transverse

forces cause bending moments to be developed in the shaft,

requiring analysis of the stress due to bending. In fact, most

shafts must be analysed for combined stress.

Keywords-:Gear shaft, Torque, Stress, Power-

transmission, Ansys, Pro-E

I. INTRODUCTION

Gear box is a speed and torque changing device

between the engine and the driving wheels. It serves

the following purposes in transmission system of an

automobile

1. It exchanges engine power for greater torque and

thus provides a mechanical advantage to drive the

vehicle at different conditions.

2. It exchanges forward motion for reverse motion.

3. It provides a neutral position to disallow power

flow to the rest of the power train.

Automobile requires high torque when climbing hills

and when starting, even though they are performed at

low speeds. On the other hand , when running at high

speeds at level roads, high torque is not required

because of momentum and it would be preferable to

have just the wheels alone turning at high speeds.

The gear box also called the transmission acts in

accordance with the running conditions. When

driving power is required, it reduces the engine speed

and transmits stronger torque to the wheels. In

addition the transmission serves to reverse the

vehicle. Since the engine can turn only in one

direction, the transmission gear can mesh in such a

manner to allow running the vehicle in reverse

direction.

Located at the junction point of a power shaft, the

gearbox is often used to create a right angle change in

direction, as is seen in a rotary mower or a helicopter.

Each unit is manufactured with a specific purpose in

mind and the gear ratio used is designed to provide

the level of force required. This ratio is fixed and

cannot be changed once the box is constructed. The

only possible modification after the fact is an

adjustment that allows the shaft speed to increase,

along with a corresponding reduction in torque.In a

situation where multiple gear speeds are needed, a

transmission with multiple gears can be used to

increase torque while slowing down the output speed.

This design is commonly found in automobile

transmissions. The gear transmission mechanism is

one of themost widely used transmission mechanism,

which canbe used to transmit the motion and force

between tworandom shafts in space of transmission,

characterizinglarge power range, high efficiency,

accuratetransmission ratio, long service life, safe and

reliable,has been widely used in various industries

(Wang et al.,2010). In which, gear shaft is the main

transmissionpart in the most general machinery and

its intensity hasa great influence on the service life of

the machine.Because the geometric structure of gear

shaft is morecomplex than the ordinary transmission

shaft, todetermine and check the actual damage

location of gearshaft by the conventional method is

documents/www.internationaljournalssrg.org



more cumbersome,it results in a bigger error (Li et

al., 2000). In order toprovide the theoretical basis for

structural design ofgear shaft, especially for new

structural measures takenfor the dangerous position

in time, the strength of gearshaft should be clearly

understood after the preliminarystructural design is

completed. Based on the abovesituation, this paper

uses the transmission systemanalysis software

MASTA to complete the strengthanalysis and

calculation for gear shaft of a certainautomobile

transmission.

II. THEORETICAL SHAFT DESIGN AND

ANALYSIS

A shaft is the component of a mechanical device that

transmits rotational motion and power. It is integral

to any mechanical system in which power is

transmitted from a prime mover, such as an electric

motor or an engine, to other rotating parts of the

system. There are many examples of mechanical

systems incorporating rotating elements that transmit

power: gear-type speed reducers, belt or chain drives,

conveyors, pumps, fans, agitators, household

appliances, lawn maintenance equipment, and parts

of a car, power tools, machines around an office or

workplace and many types of automation equipment.

Visualize the forces, torques, and bending moments

that are created in the shaft during operation. In the

process of transmitting power at a given rotational

speed, the shaft is inherently subjected to a torsional

moment, or torque. Thus, torsional shear stress is

developed in the shaft. Also, a shaft usually carries

power-transmitting components, such as gears, belt

sheaves, or chain sprockets, which exert forces on the

shaft in the transverse direction (perpendicular to its

axis). These transverse forces cause bending

moments to be developed in the shaft, requiring

analysis of the stress due to bending. In fact, most

shafts must be analysed for combined stress.

Because of the simultaneous occurrence of

torsional shear stresses and normal stresses due to

bending, the stress analysis of a shaft virtually always

involves the use of a combined stress approach. The

recommended approach for shaft design and analysis

is the distortion energy theory of failure. Vertical

shear stresses and direct normal stresses due to axial

loads also occur at times, but they typically have such

a small effect that they can be neglected. On very

short shafts or on portions of shafts where no bending

or torsion occurs, such stresses may be dominant.

A. Procedure for Design and analysis of a Shaft

1. Determine the rotational speed of the shaft, n

(rpm).

2. Select the material from which the shaft will be

made, and specify ultimate tensile strength Su,

yield strength Syand its surface condition:

ground, machined, hot-rolled and as-forged. At

the moment, due to lack of database for

endurance strength, this module should be used

in the design and analysis of steel shafts only.

Use the database in selection of a material.

3. Apply a desired reliability for definition of

reliability factor, CR.

4. Apply a design factor, N (we prefer to use ηd).

5. Propose the general form of the geometry for the

shaft, considering how each element on the shaft

will be held in position axially and how power

transmission from each element to the shaft is to

take place. Design details such as fillet radii,

shoulder heights, and key-seat dimensions must

also be specified. Sometimes the size and the

tolerance for a shaft diameter are dictated by the

element to be mounted there. For example, ball

bearing manufacturers' catalogs give

recommended limits for bearing seat diameters

on shafts.

6. Specify the location of bearings to support the

shaft. The reactions on bearings supporting radial

loads are assumed to act at the midpoint of the

bearings. Another important concept is that

normally two and only two bearings are used to

support a shaft. They should be placed on either

side of the power-transmitting elements if




possible to provide stable support for the shaft

and to produce reasonably well-balanced loading

of the bearings. The bearings should be placed

close to the power-transmitting elements to

minimize bending moments. Also, the overall

length of the shaft should be kept small to keep

deflections at reasonable levels.

7. Determine the design of the power-transmitting

components or other devices that will be

mounted on the shaft, and specify the required

location of each device.

8. Determine the power to be transmitted by the

shaft.

9. Determine the magnitude of torque at point of the

shaft where the power-transmitting element is.

T = 30 H/π n [N-m]

where:

H = transmitted power, W

T = torque, N-m.

n = rotational speed, rpm.

10. Determine the forces exerted on the shaft.

Spur and helical gears, tangential force

Wt = 60 000 H / π d n

[N]

where: d = pitch diameter of gear in [mm];

H = Power in [W];

N = Rotational Speed in [rev/min]

Radial force ; Wr = Wt. tan φn / cos ψ [N]

where: = normal pressure angle for helical

gears, and pressure angle for spur gears; and

ψ = helix angle

11. Preparing a torque diagram.

12. Resolve the radial forces into components in

perpendicular directions, vertically and

horizontally.

13. Solve for the reactions on all support bearings in

each plane.

14. Produce the complete shearing force and bending

moment diagrams to determine the distribution of

bending moments in the shaft.

15. Analyze each critical point of the shaft to

determine the minimum acceptable diameter of

the shaft at that point in order to ensure safety

under the loading at that point. In general, the

critical points are several and include those

where a change of diameter takes place, where

higher values of torque and bending moment

occur, and where stress concentrations occur.

If a vertical shearing force V is the only significant

loading present, this equation should be used to

compute the required diameter for a shaft.

where:

Kt = stress concentration factor at the shoulder;

1.5 to 2.5;

V = Vertical Shear Force [N];

N = Factor of Safety / Design Factor

(you may use ηd);

D or d = Diameter of the Shaft at the

section considered [mm];

S’n = modified endurance strength [MPa],

(Which depends on ultimate tensile strength Su).

where:

Cs = size factor;

CR = reliability factor;

Sn = endurance strength [MPa]

In most shafts, the resulting diameter will be much

smaller than that required at other parts of the shaft

where significant values of torque and bending

moment occur. Also, practical considerations may

require that the shaft be somewhat larger than the

computed minimum to accommodate a reasonable

bearing at the place where the shearing force V is

equal to the radial load on the bearing.

Most shafts are subjected to bending and torsion. The

power being transmitted causes the torsion, and the

transverse and radial forces on the elements cause

n

'

.

n

t

S

NVKD

942

RSnn CCSS '




bending. In the general case, the transverse forces do

not all act in the same plane. In such cases, the

bending moment diagrams for two perpendicular

planes are prepared first. Then the resultant bending

moment at each point of interest is determined.

A design equation is now developed based on the

assumption that the bending stress in the shaft is

repeated and reversed as the shaft rotates, but that the

torsional shear stress is nearly uniform.

Where:

M = Bending moment (a resultant obtained

from bending moment diagrams; (this creates

reversed bending stresses on the shaft) [N-mm];

T = Torsion or twisting moment (usually

steady) [N-mm];

N = Factor of safety; (We shall usually use η.)

D = Diameter of the shaft at the section under

investigation; in [mm].

Also, Sy and Sn are to be taken as [MPa]

III. DESIGNING OF GEAR SHAFT

A. Shaft Design

A shaft is the component of a mechanical device

that transmits rotational motion and power. It is

integral to any mechanical system in which power

is transmitted from a prime mover, such as an

electric motor or an engine, to other rotating parts

of the system. There are many examples of

mechanical systems incorporating rotating

elements that transmit power: gear-type speed

reducers, belt or chain drives, conveyors, pumps,

fans, agitators, household appliances, lawn

maintenance equipment, and parts of a car, power

tools, machines around an office or workplace

and many types of automation equipment.

Preprocessor

• Member length.

• Member position.

• Member material.

• Element type -- SOLID 8 NODE 185

• Material model -- AL ALLOY

• Real constants -- NONE

• Meshing -- TETRA FREE

• Loads -- MODAL LOADS

Solution

• Load position.

• Load magnitude.

• Load direction.

• SOLUTION --- Solve - current L.S (Solves

the problem)

Post-processor

• Get displacement member force detain both

graphical and text output.

•Plot results – contour plot -- nodal solution

IV. RESULTS OF ANSYS MODEL

3

1

22

4

332

yn

t

S

T

S

MKND

'




INPUT GEAR SHAFT ANSYS MODEL

MESHED MODEL

SHAFT NODAL SOLUTIONS

MAXIMUM ABSOLUTE VALUES

NODE 7061 8212 930

VALUE 0.31897

E-04

0.14851E-

05

0.15517E-

03

SHAFT STRESS INTENSITY

MINIMUM VALUES

NODE 1542 1542 1542

VALUE 0.12954

E+06-0

0.16107E+

06

0.44095E+

06

VON MISES STRESS

V. CONCLUSIONS

.The model that is created in Pro/Engineer wildfire

5.0 and analysed in Ansys V12.1. The model created

in Pro/Engineer is transferred to Ansys through IGES

(Initial Graphics Exchange Specification) format.

The structural analysis has been performed on the

model by applying the proposed material properties,

boundary conditions and loads. By viewing the

results that has been discussed in the early chapter, it

can be said that the input gear shaft model can




withstand the proposed loads with considering a

factor of safety as 1.2. So, thereafter the designed

model can be manufactured or fabricated with

extensive testing.

References

1. Design of machine elements – v.m faires

2. Machine design –schaum series

3. Machine design –Pandya& shah

4. Design data book-psg

5. Mech engg design – j.e shigley

6. Automotive mechanics – kripal singh

BIODATA

AUTHOR1

SingiReddy Ravinder has received the

B.Tech (MechanicalEngineering) Degree

fromAVN institute of Science and

Technology, Rangareddy and

pursuingM.Tech (Machine Design) in

VIST, Bhoingiri, Nalgonda, Telangana, India.

AUTHOR2

Ramesh Banothu has 5 years experience

in teaching in

graduate and post graduate level and he

presently working as Associate Professor

and HOD of Mechanical Department in

VIST, Bhoingiri, Nalgonda, Telangana,

India.


Documents

Design and analysis of Gear Shaft - SSRG-Journalsinternationaljournalssrg.org/IJME/2015/Volume2-Issue9/IJME-V2I9P... · Design and analysis of Gear Shaft ... mechanical advantage