Design of Shafts

PEMP

MMD2512

MTDT2512

M.S. Ramaiah School of Advanced Studies, Bengaluru

Design of Machine Elements- SHAFTS

Session delivered by:

Mr. Nithin Venkataram

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MMD2512

MTDT2512


Session Objectives

At the end of this session students would have understood,

• Introduction to shafts

•Materials used in shaft.

•Types of shaft.

•Design criteria for shafts.

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Session Topics

• Introduction

• Materials used for shafts

• Types of shaft.

• Stresses in Shafts

• Shafts Subjected to Twisting Moment Only

• Shafts Subjected to Combined Twisting Moment

and Bending Moment

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Introduction

• A shaft is a rotating machine

element which is used to transmit

power from one place to another.

• The power is delivered to the shaft by some tangential

force and the resultant torque (or twisting moment) set up

within the shaft permits the power to be transferred to

various machines linked up to the shaft.

• The shaft must not only be strong enough to provide an

adequate FOS from static and dynamic stress view points

and it must also be sufficiently rigid to prevent torsional

and lateral deflection.

• The shaft natural frequency of vibration must be

sufficiently remote from the operating frequency to avoid

resonance. 4

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Material Used for Shafts

The material used for shafts should have the following

properties :

1. It should have high strength.

2. It should have good machinability.

3. It should have low notch sensitivity factor.

4. It should have good heat treatment properties.

5. It should have high wear resistant properties.

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Types of Shafts

The following two types of shafts are important from the

subject point of view:

1. Transmission shafts.

– These shafts transmit power between the source and the

machines absorbing power.

– The counter shafts, line shafts, over head shafts and all

factory shafts are transmission shafts.

– These shafts carry machine parts such as pulleys, gears etc.

2. Machine shafts.

– These shafts form an integral part of the machine itself.

– The crank shaft is an example of machine shaft.

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Stresses in Shafts

The following stresses are induced in the shafts :

1. Shear stresses due to the transmission of torque (i.e. due

to torsional load).

2. Bending stresses (tensile or compressive) due to the

forces acting upon machine elements like gears, pulleys

etc. as well as due to the weight of the shaft itself.

3. Stresses due to combined torsional and bending loads.

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Shafts Subjected to Twisting Moment Only

• When the shaft is subjected to a twisting moment (or

torque) only, then the diameter of the shaft may be

obtained by using the torsion equation.

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• When the hallow shaft is considered, the polar moment of

inertia becomes

• The torque equation becomes

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Shafts Subjected to Bending Moment Only

• When the shaft is subjected to a bending moment only, then

the maximum stress (tensile or compressive) is given by the

bending equation

• Substituting the values into bending equation

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Shafts Subjected to Combined Twisting

Moment and Bending Moment

• When the shaft is subjected to combined twisting moment

and bending moment, then the shaft must be designed on the

basis of the two moments simultaneously.

• Various theories have been suggested to account for the

elastic failure of the materials when they are subjected to

various types of combined stresses

• The following two theories are important from the subject

point of view

1. Maximum shear stress theory or Guest's theory. It is used for

ductile materials such as mild steel.

2. Maximum normal stress theory or Rankine’s theory. It is used for

brittle materials such as cast iron.

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• According to maximum shear stress theory, the maximum

shear stress in the shaft

• Substituting the values

• The expression under the root is known as equivalent

twisting moment and is denoted by Te.

• From this expression, diameter of the shaft (d) may be

evaluated.

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• According to maximum normal stress theory, the maximum

normal stress in the shaft,

• The expression on the RHS is known as equivalent

bending moment and is denoted by Me.

• From this expression, diameter of the shaft (d) may be

evaluated.

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Shear force and bending moment diagram

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P w

a

L

b

x1

x2

x3

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M.S. Ramaiah School of Advanced Studies, Bengaluru 15

1. Positive Shear Force will cause a

clockwise rotation of the member on

which it acts.

2. Positive Bending Moment will cause

compression on the top surface of the

beam.

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Positive Shear

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Positive Moment

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Critical Point identification

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Critical Speed of shaft.

• For a central disc of weight W on the shaft of negligible

weight rotating in antifriction bearing and shaft is simply

supported.

• Central disc of weight W on the shaft of negligible weight

rotating in sleeve bearing & shaft is assumed to be fixed-

ended

• Disc mounted at a distance a from left support and b from the

right support.

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Summary

• The following are explained,

– Common shaft loading mechanisms

– Shaft design characteristics

– Attachments and Stress concentrations

– Shaft Design: General considerations

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Documents

Design of Shafts