International Journal of Engineering and Management Research, Volume-3, Issue-2, April 2013
ISSN No.: 2250-0758
Pages: 22-30
www.ijemr.net
Design and Analysis of Rotor Shaft Assembly of Hammer Mill Crusher
E.Vijaya Kumar
Assistant Professor, Department of Mechanical Engineering, Siddhartha Institute of Technology & Sciences, Ghatkesar, Hyderabad, INDIA
ABSTRACT
The paper deals with the Design and analysis of shaft and rotor assembly for hammer mill crusher of capacity 0.1
(100kg/hr) tones per hour transmitting 20 B.H.P and a speed of 750 rpm. The design is based on the standard design procedure.
In the present work by using the standard design procedure, diameter of rotor shaft of hammer mill crusher has been designed. The
design should be safe when the values obtained from the present design procedure were compared with the values and results
obtained from the analysis using Ansys package.
When the shaft is rotated at rated speed (rpm) and the loads applied to the shaft it should not bend during rotation. When
the shaft is rotated under free conditions, deflections will be created due to the critical speed of the shaft.
To compare this deflection shaft was designed such that the natural frequency and speed is under limits. In this project the shaft and
rotor assembly of hammer mill crusher was modeled using Pro-e modeling package and the FEM model of the shaft was developed
using Ansys package. Meshing of the shaft model was done and the loads, stresses that were applied for the shaft to be checked out
that the design should be safe one.
I. INTRODUCTION
A crusher is a machine designed to
reduce large solid material objects into a smaller
volume, or smaller pieces. Crushers may be used
to reduce the size, or change the form, of waste
materials so they can be more easily disposed of
or recycled, or to reduce the size of a solid mix
of raw materials (as in rock ore), so that pieces of
different composition can be differentiated.
Crushing is the process of transferring a force
amplified by mechanical advantage through a
material made of molecules that bond together
more strongly, and resist deformation more, than
those in the material being crushed do. Crushing
devices hold material between two parallel
or tangent solid surfaces, and apply sufficient
force to bring the surfaces together to generate
enough energy within the material being crushed
so that its molecules separate from (fracturing),
or change alignment in relation to (deformation),
each other. The earliest crushers were hand-held
stones, where the weight of the stone provided a
boost to muscle power, used against a stone
anvil. Querns and mortars are types of these
crushing devices.
II. WORKING OF MACHINE
When coal is delivered to the hammer mill
crusher, it is prepared for cyclone furnace firing
by being crushed into 1/4 inch or smaller size
coal. Coal enters from the top and is violently
thrown against the breaker blocks by the
hammers. The final crushing is done between the
hammer faces and the screen bars. Then the
crushed coal goes to the conveyors below and is
carried to the storage bunker. Tramp iron or
material that will not go out between the screen
bars is dropped into the iron pocket and is later
removed. The final crushing is done between the
hammer faces and the screen bars. Then the
crushed coal goes to the conveyors below and is
carried to the storage bunker. Tramp iron or
material that will not go out between the screen
bars is dropped into the iron pocket and is later
removed.
Hammer mill features:
 Material is reduced by impact from
free-swinging bar hammers
 Finished Product size controlled by
grates or crusher sizes
 Materials can be reduced to granular
powder at high rate.
 Heavy-duty cast-iron or carbon steel
construction
 Right-hand or left-hand machine
available
 Easy access for maintenance and
crusher/grate change
Applications of Hammer mill crushers:
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Material used for Shafts:
 Recycling glass
 Feed industry
 Stone crushing
 Size reduction of waste materials
 Electronics recycling
 Ceramics
 Pulverization of sea shells
 Minerals
 Wood particles for fuel wood
 Limestone
III.
DESIGN OF SHAFT
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 machine
linked up to the shaft.
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 element like gears,
pulleys etc.
3. Stresses due to combined torsional and
bending loads.
IV.
CLASSIFICATION OF
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.
4. It should have good heat treatment
property.
5. It should have high wear resistant
property.
Depending on the requirement, the shafts can be
made of plain carbon steel or alloy steel.
Designing of Shafts:
The shafts may be designed on the basis of
1) Strength and 2) rigidity and stiffness
In designing shafts on the basis of strength, the
following cases may be considered:
1) Shafts subjected to twisting moment or
torque only.
2) Shafts subjected to bending moment
only.
3) Shafts subjected to combined twisting
and bending moment
4) Shafts subjected to axial loads in
addition to combined torsion &
bending loads
Shafts subjected to twisting moment or
torque only:
When the shaft is subjected to twisting
moment (or torque) only, then the diameter of
the shaft may be obtained by using the torsion
equation. We know that
SHAFTS
Shafts involved in power transmission may be
classified as
1) Transmission shafts are used to transmit
power between source and the machines using
the power. They include line shafts, jackshafts
and counter shafts.
i) Line shaft is a long continuous
shaft, which receives power from
the source and distribute to
different machines.
ii) Jackshaft is directly connected to
the source of power and from
which other shafts are driven.
iii) Counter shafts receive power from
line shaft and transmit to a
machine.
2) Machine Shafts are incorporated within the
machine, such as crank shaft
Where,
T=Twisting moment acting on the shaft,
J=Polar moment of inertia of the shaft
about the axis of rotation,
F s =Torsional shear stress, and
r=Distance from neutral axis to the outer
most fiber
=d/2 where
We know for round solid shaft, polar moment of
inertia,
The equation may be written as
T/πd4= 2f s /32d
T = f s πd3/ 16
Twisting moment (T) may be obtain by the
following relation:
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In S.I units, power transmitted (in watts) by the
shaft,
P=2πNT/60
or
T=(P х 60)/2πN
Where,
T=Twisting moment in N-m
N=Speed of the shaft in RPM
In M.K.S units, horse power transmitted by the
shaft,
P=2πNT/4500
T=P х 4500/2πN
Where,
T=Twisting moment in N-m and
N=Speed of the shaft in rpm
1) Guest’s Theory: According to maximum
shear stress theory the maximum shear stress due
to combined load is
Let
f s = Shear stress induced to
twisting moment
f b = bending stress (tensile or
compressive) induced to Bending moment
According to Maximum shear stress theory, the
maximum shear stress in the shaft
f s ( max) =√[( f b )2 + 4(f s )2]
Substituting the values of f b & f s as per above
equations
Shafts subjected to bending moment only:
πd3 х f s = 16 х √ (M2+T2)
f s =√ (32M/ πd3)2+4(16T/ πd3)
When the shaft is subjected to a bending moment
only, then the maximum stress (tensile or
compressive) is given by the bending equation.
We know that
3) Rankine’s Theory: According to
maximum normal stress theory, the
maximum normal stress in the shaft
Where,
M=Bending moment, N-mm
I=Moment of inertia of cross-sectional
area of the shaft about the
Axis of rotation, mm4
F b =Bending stress, N/mm2 and
Y=Distance from neutral axis to the
outer-most fiber, mm
We know that, Moment of Inertia, for a round
solid shaft
and
I = πd4 /64
y = d/2
Substituting these values in the above equation
Bending Moment
M= (πd3 /32) х fb
Shafts subjected to combined twisting and
bending moment:
When the shaft is subjected to combined
twisting and bending moment then the shaft must
be designed on the basis of the two moments
simultaneously. The maximum induced stress
can be obtained by considering the following
theories.
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
Rankin’s theory. It is used for brittle
materials such as cast iron.
f b (max) = (f b /2) +√ [( f b )2 +4(f s )2]
f b = (16/ πd3) х (M+√ (M2+T2))
Shafts subjected to fluctuating loads:
In above equations shafts are subjected to
constant twisting moment & bending moment
but in actual practice shafts are subjected to
fluctuating torque & bending moments. In order
to design such shafts like line shaft &counter
shaft combined shock & fatigue factor to be
considered for calculating33 twisting moment
and bending moment
Substituting these factors in above equations
For maximum shear stress theory
(πd3/16) х f s =√ [(K m хM)2+ (K t хT)2] =T e
For maximum normal (tensile or
compressive) theory
(πd3/16) х f s = [(K m хM) /2] +√ [(K m хM)
2
+ (K t хT) 2] =M e
Where:
M= Bending Moment
f b = Bending stress
T = Twisting moment (Torque)
upon the shaft
f s = Tensional shear stress
K m = Combined shock &
fatigue factor for bending
K t -= Combined shock &
fatigue factor for twisting
d = diameter of the shaft
Shaft calculations:
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We know
Given Data:
Π /16 х f s х d³ =√ [(K m х M)²+(K t х T)²]
•
Power transmitted by the shaft=75kw or
100hp
•
Speed of the shaft =750 rpm
•
Weight of the rotor shaft =2000kg
•
Beam length =165cm
•
Arm length =27cm
Actual deflection δ = (Wl³/384) х E х I
•
Shear stress =650 kg/cm²
=
2000/384x2.1x10^6x1198.4
•
Bending stress =300 kg/cm²
Π /16 х 650 х d³
=√[(2x54000)²+(2x9549) ²]
d=9.5cm (or) 95mm
Deflection of Shaft:
= 0.009246cm
Twisting Moment:
Allowable deflection = L/1500
Power p=2πNT/4500
= 0.11cm
100= (2π х 750 х T)/4500
Factor of safety = Allowable deflection
/ Actual deflection
T=95.49 kg-m (or) 9549 kg-cm
We know
= 0.11/0.009246
T= (π/16) х f s х d³
= 11
9549= π /16 х 650 х d³
Selected diameter of shaft =122.7mm ≈
125mm
d=4.21 cm (or) 42.1mm
Bending Moment:
M =Weight of Screen х Arm Length
= 4500 х 27
=54000 kg-cm
We know
M = (π /32) х f b х d³
54000= π /32 х 300 х d³
d=12.2cm (or) 122.3mm
Combined Bending and Twisting Moment:
We know that
Π /32 х f b х d³= [M+√M²+T²]/2
Π /32 х 300 х d³= [54000 +√ (54000²+9549²)]/2
d=12.2cm (or) 122.7 m
Fluctuating Loads:
V.
DESIGN OF BEARINGS
A bearing is a machine element, which
supports another moving machine element,
knows as journal. It permits a relative motion
between the contact surfaces of the member,
while carrying the load. The efficiency of the
mechanical system depends to a great extent on
the efficiency of its bearings.
A necessity for the efficient working of the
bearings is that the running surface should be
adequately supplied with lubricant. For this
purpose the oil is supplied through a lubricating
ring firmly clamped on the shaft at the after end
and a wiper device fitted in the upper part. This
device, together with correctly formed oil
grooves in the bearing shells ensure that in
bearings the oil supply is maintained in all
circumstances even at low revolutions.
VI.
SPHERICAL ROLLER
BEARING
A spherical bearing is a bearing that
permits angular rotation about a central point in
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two orthogonal directions within a specified
angular limit based on the bearing geometry.
Typically these bearings support a rotating shaft
in the [bore] of the inner ring that must move not
only rotationally, but also at an angle.
Construction of spherical bearings can be
hydrostatic or strictly mechanical. A spherical
bearing by itself can consist of an outer ring and
an inner ring and a locking feature that makes the
inner ring captive within the outer ring in the
axial direction only. The outer surface of the
inner ring and the inner surface of the outer ring
are collectively considered the raceway and they
slide against each other, either with a lubricant or
a maintenance-free based liner. Some spherical
bearings incorporate a rolling element such as a
race of ball bearings, allowing lower friction.
The design of this bearing permits radial load
and heavy thrust load in either direction.
Fig. Spherical Roller Bearing
VII.
BEARING LIFE CALCULATION
Type of bearings used: spherical roller bearings
Selected diameter of the shaft=125mm
N=speed of the shaft=750 r.p.m
L h =nominal/rated speed in hours =10000 hrs, 10hrs per a day heavy shock load
Then life of bearing in millions of revolutions
L=60NL h /106
L= (60 х 750 х 10000)/106
L=4500 millions of revolutions
Where L is life that 90% of a group of apparently identical group of bearings will complete
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Fig Rotor Assembly with Bearings
VIII. ELEMENT USED FOR ANALYSIS
BEAM3 is a uni-axial element with tension, compression, and bending capabilities. The element has
three degrees of freedom at each node: translations in the nodal x and y directions and rotation about the
nodal z-axis. Other 2-D beam elements are the plastic beam.
2D Beam Analysis:
Fig Deformed Shape
Fig Von Mises Stress
3D Shaft Analysis:
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Fig Deformed Shape
Fig: Rotor Shaft Assembly Mesh in Ansys
Fig: Deformations in Ansys
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Fig. Von Mises Stress
Now we can see the stresses in shaft.
Maximum stress developed in shaft is 36.15
N/mm2 which is far less than the yield strength
of the material, which is 45 N/mm2. So that shaft
will not fail under these conditions
10.As per analysis of shaft and rotor
assembly done in Ansys, deflection values
of the shaft and rotor assembly are 0.008637
and 0.006404.
REFERENCES
IX.
CONCLUSIONS
1.
As per drawings and information provided
by Bevcon, 3D models are developed in Pro-e
and the shaft of crusher is analyzed in Ansys
package.
1. Based on calculations and analysis
reports the safe diameter is selected as
125mm, which is safe.
2. Factor safety for selected diameter is
11. This factor of safety chosen for
crusher to address sudden impact and
shock loads created by the material.
3. Deflection of shaft as per theoretical
calculations is 0.009mm.
4. Deflection of shaft in Ansys analysis is
0.007mm (load applied on shaft only).
5. Deflection of total rotor assembly in
Ansys is 0.006mm.
6. Selected bearing for this application
based on shaft diameter 125mm is
heavy-duty spherical roller bearings on
adapter sleeve.
7. 3D models developed in pro-e
& analyzed reports have been
submitted to Bevcon for their
consideration in their designs
8. We suggested to consider this analysis
report to reduce the bearing diameter
metal for optimizing the rotor design
of the hammer mill crusher.
9. Bearing life for selected bearings is 450
Millions of revolutions.
Scham Tickoo, “Pro-Engineer2001”, 2nd edition.
2. J.N.Reddy, “An Introduction
to Finite Element Method”, 3rd
edition.
3. R.K.Allan,“Rolling Bearing “,
3rd edition
4. S.S.Rao, “Mechanical
Vibrations’’, 4th edition.
5. Richard G.Budynas Jata,
“Advanced Strength and
Applied Stress Analysis”, 2nd
edition
.
6. V.B. Bhandari, “Introduction
to Machine Design”.
7. Robert L.Norton, “Machine
Design”, 2nd edition.
8. Hall, Holowenko Laughlin,
“Theory and Problem of
Machine Design”, Schanm’s
series.
9. PERRY, r.h., and d.w.Green,
“Perrys Chemical Engineers”
handbook, “7th ed.
10. F.D.Bond, “Crushing
Calculations”.
11. Pennsylvania, “Crushing
Technologies”.
12. P.C.Hayes, “Construction of Hammer
Mill Crusher”.
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