57 DESIGN OF SOLID SHAFTS USING MATLAB - IAEME OF SOLID SHAF… · DESIGN OF SOLID SHAFTS USING ... Design of shaft primarily involves in determining stresses at critical ... BENDING

International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print),

ISSN 0976 – 6359(Online) Volume 3, Issue 3, Sep- Dec (2012) © IAEME

645

DESIGN OF SOLID SHAFTS USING MATLAB

GOPICHAND ALLAKA Head of Department, Department of Mechanical engineering,

Swarnandhra College of Engineering & Technology, Andhra Pradesh

Email: allakagopichand @gmail.com

PRASAD RAJU KALIDINDI

IV Year, B.Tech, Department of Mechanical engineering


Email:[email protected]

KOTESWARA RAO S IV Year, B.Tech, Department of Mechanical engineering


MANIBABU DAADI IV Year, B.Tech, Department of Mechanical engineering


ABHAY PATNALA

IV Year, B.Tech, Department of Mechanical engineering


ABSTRACT

Shaft is a most common and important machine element. Shafts are widely used

mechanical components which are used to transmit power through devices such as gears and

pulleys. The shaft is generally acted upon by bending moment, torsion and axial force.

Design of shaft primarily involves in determining stresses at critical point in the shaft that is

arising due to aforementioned loading. The friction and other losses in this type of power

transmission equipment are comparatively very low.

In this paper we use a software called “MATLAB” to write a program to design a

shaft. MATLAB is extensively used for scientific and research purposes. It is accurate and

also has a number of built in functions which makes it versatile. Still MATLAB is not

effectively being used in mechanical engineering field. At present the MATLAB code for

design of shafts doesn’t exists. Our MATLAB code works for all solid shafts mounted with

number of pulleys and gears. The program is user friendly one & when executed it ask the

inputs and performs the necessary design calculations and gives necessary output values. We

INTERNATIONAL JOURNAL OF MECHANICAL ENGINEERING

AND TECHNOLOGY (IJMET) ISSN 0976 – 6340 (Print) ISSN 0976 – 6359 (Online) Volume 3, Issue 3, September - December (2012), pp. 645-653

© IAEME: www.iaeme.com/ijmet.asp Journal Impact Factor (2012): 3.8071 (Calculated by GISI) www.jifactor.com

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have taken both maximum shear stress theory and maximum normal stress theory into

consideration. It also generates the diagrams for horizontal, vertical and resultant bending

moments over the lengths of the shaft. As computers are used to perform the task of shaft

design becomes simple, fast, friendly and error free.

Keywords: shaft design, MATLAB, bending moments, torque, diameter.

1. INTRODUCTION

1.1 SHAFTS A shaft is a rotating member, usually of circular cross-section, used to transmit power

or motion and to support components like gears, pulleys etc. Shafts must have adequate

torsion strength to transmit torque and not to be over stressed. Components such as gears are

mounted on shafts using keys. Shaft must sustain a combination of bending and torsion loads.

1.2 STANDARD SIZES OF SHAFTS Typical sizes of solid shaft that are available in the market are,

� Up to 25 mm 0.5 mm increments

� 25 to 50 mm 1.0 mm increments



1.3 MATERIAL FOR SHAFTS The ferrous, non-ferrous materials and non metals are used as shaft material

depending on the application. Some of the common ferrous materials used for shaft are

discussed below.

1.3.1 Hot-rolled plain carbon steel

These materials are least expensive. Since it is hot rolled, scaling is always present on

the surface and machining is required to make the surface smooth.

1.3.2 Cold-drawn plain carbon/alloy composition Since it is cold drawn it has got its inherent characteristics of smooth bright finish.

Amount of machining therefore is minimal. Better yield strength is also obtained. This is

widely used for general purpose transmission shaft.

1.3.3 Alloy steels

Alloy steel as one can understand is a mixture of various elements with the parent

steel to improve certain physical properties. To retain the total advantage of alloying

materials one requires heat treatment of the machine components after it has been

manufactured. Nickel, chromium and vanadium are some of the common alloying materials.

However, alloy steel is expensive.

These materials are used for relatively severe service conditions. When the situation

demands great strength then alloy steels are used. They have fewer tendencies to crack, warp

or distort in heat treatment. Residual stresses are also less compared to CS (Carbon Steel).



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2. DESIGN OF SHAFT

When the shaft, carrying heavy pulleys, gears or some loads, transmits power, it is

said to be subjected to combined torque and bending moment. In this case, the shaft may be

designed based on two theories.

1. Guest’s theory (or) Maximum shear stress theory.

2. Rankine’s theory (or) Maximum normal stress theory.

Let Ss = Torsion shear stress due to pure bending moment, (T)

Sb =Bending stress induced due to pure bending moment, (M)

2.1 Maximum shear stress theory:

According to this theory, the equivalent torque is given by

Te = � �� Ss ��

Where Te = √� � is known as Equivalent torque.

2.2 Maximum normal stress theory:

According to this theory, the equivalent bending moment is given by

Me = � � Sb ��

Where Me = �� √� � is known as Equivalent bending moment.

Generally, the Guest’s theory will be used for ductile material and Rankine’s theory

will be used for brittle material.

For designing of shaft, the diameter is calculated based on both theories and the larger

value will be chosen.

In actual practice, the torque and bending moment may not be constant because of

change of power and loads due to voltage variations, and the surroundings nature like non-

uniformity of roads as in case of automobiles and so onm. Hence for designing such shafts,

subjected to this type of fluctuating loads, certain safety factors called shock and fatigue

factors may be taken into account.

Let Km = Combined shock and fatigue factor for bending.

Kt = Combined shock and fatigue factor for torsion.

By including the above factors, the equivalent torque Te, may be changed as

Te = ��.� ��. �

And the equivalent bending moment Me, may be changed as

Me = ��.� ��.� ��. �



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Table: Shock and Fatigue factors

Nature of load Km Kt

1. Stationary shafts : (i) Gradually applied load 1.0 1.0

(ii) Suddenly applied load 1.5 to 2.0 1.5 to 2.0

2. Rotating shafts :

(i) Gradually applied load 1.5 1.0

(ii) Suddenly applied load with minor shock 1.5 to 2.0 1.0 to 1.5

(iii) Suddenly applied load with major shock 2.0 to 3.0 1.5 to 3.0

3. ABOUT MATLAB

MATLAB stands for MATrix LABoratory. Hence, as the name suggests, here you play around with

matrices. MATLAB is a numerical computing environment and fourth-generation programming language.

Developed by Math Works, MATLAB allows matrix manipulations, plotting of functions and data,

implementation of algorithms, creation of user interfaces, and interfacing with programs written in other

languages, including C, C++, Java and FORTRAN.

There are 4 main windows:

Command window: This is the main window where you write the commands, as well as see the outputs. In

other words, here is your interaction with the software.

Command History: As the name suggests, it shows the list of the commands recently used in chronological

order. Hence, you can double click on a command to execute it again.

Current directory: It is the default directory (folder) for saving your files. All the files which you make (like

m-files) are saved here and can be accessed from here directly. The location of the current directory is shown in

the toolbar at the top. You can change it by changing the address here.

Workspace: It displays the list of the variables defined by you in the current session of MATLAB.

4. DESIGN OF SHAFT USING MATLAB

In this paper we designed a MATLAB code and a MATLAB script file is developed to design a solid

shaft mounted with gears and pulleys and generates bending moment diagrams.

Inputs used in this work are speed, length of the shaft, diameter, weight, and power for gears and pulleys,

distances of pulleys and gears to the right of the left hand bearing, allowable shear and tensile stresses for the

given shaft material.

4.1 MATLAB OUTPUT WINDOW

The MATLAB code we designed takes the input values as shown in below figure and the logic that we

have formulated gives the output values such as torque, tangential, radial force for gears, torque, total vertical

and horizontal loads for pulleys and maximum bending moments, torques and the final standard diameter of the

shaft.

It also generates horizontal, vertical and resultant bending moment diagrams over the length of the

shafts.

We are solving an example problem 4.15 in page number 4.53 from “Machine Design” by

S.Md.Jalaludeen textbook.

4.2 PROBLEM 4.15: A solid shaft is supported on two bearings 2 meters apart and rotates at 500 rpm. Two pulleys whose

diameters measuring 800 mm and 600 mm respectively are mounted on the shaft at distances 400 mm and 1200

mm respectively to the right of the left hand bearing. A 20° involute gear of 300 mm diameter is keyed to the

shaft at a distance of 200 mm to the left of right hand bearing. A power of 50 kW is supplied to the gear, out of

which 30 kW is transmitted by bigger pulley weighing 600 N and 20 kW is transmitted to the smaller pulley

whose weight measures 450 N. The drive from bigger pulley is vertically downward and from smaller pulley is

horizontal. The tension ratio for both pulleys is 2. Design the shaft for the working stress of 45 Mpa in shear and

80 Mpa in tension. Assume the combined shock and fatigue factors for bending and torsion as 2 and 1.5

respectively.

International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976

ISSN 0976 – 6359(Online) Volume 3, Issue 3, Sep

4.3 SOLUTION USING MATLAB:


6359(Online) Volume 3, Issue 3, Sep- Dec (2012) © IAEME

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MATLAB:

COMMAND WINDOW 1






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COMMAND WINDOW 2






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COMMAND WINDOW 3






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COMMAND WINDOW 4




The inputs are to be given whenever asked in the correct units specified. The

horizontal, vertical and resultant bending moment diagrams generated by MATLAB code are

BENDING MOMENT DIAGRAM FOR THE ABOVE PROBLEM

5. CONCLUSION

The answers generated by MATLAB code are verified with the textbook answers and

are proved to be correct.Our MATLAB code also works for any solid shaft simply supported

on bearings carrying number of gears and pulleys.

6. REFERENCES

[1] Shigley, J.E. and Uicker,J.J.,Theory of machines and mechanisms,

[2] R.S. KHURMI and J.K. GUPTA, Theory

reprint (2008), pp.382-397

[3] Rudra Pratap,’ Getting started with MATLAB

Version 7.8 (2009).

[4] “Machine Design” by S.Md.Jalaludee

[5] “Design Data Hand Book for Mechanical Engineers” By K.Mahadevan

Reddy.



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on bearings carrying number of gears and pulleys.

d Uicker,J.J.,Theory of machines and mechanisms, McGraw-

GUPTA, Theory of machine�, S. Chand publications, Edition

Getting started with MATLAB, Oxford university Press, updated for

[4] “Machine Design” by S.Md.Jalaludeen, Anuradha Publications (2009)

[5] “Design Data Hand Book for Mechanical Engineers” By K.Mahadevan & K.Balaveera







-Hill, 1986

, S. Chand publications, Edition 16

, Oxford university Press, updated for

K.Balaveera

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57 DESIGN OF SOLID SHAFTS USING MATLAB - IAEME OF SOLID SHAF… · DESIGN OF SOLID SHAFTS USING ... Design of shaft primarily involves in determining stresses at critical ... BENDING