09 flex me chele
TRANSCRIPT
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09 Flexible Mechanical Elements9.0 Introduction
9.1 Belts
9.1.1 Flat and Round-Belt Drives
9.1.2 The Contact Angles
9.1.3 The Steps in Analysing a Flat-Belt Drive9.2 Chains
9.2.1 The Advantages of Chains
9.2.2 The Application of Chain Drives
9.2.3 Drive Design9.2.4 Chain and Sprocket Design
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Introduction
Belts, ropes, chains and other similar elastic orflexible machine elements are used in conveying
systems and in the transmission of power over
comparatively long distances.
The use of these elements simplifies the designof a machine and substantially reduces the cost.
These elements are elastic and usually quite
long, they play an important part in absorbing
shock loads and in damping out and isolating the
effects of vibration.
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Belts
Characteristics of some common belt types
Belt Type Figure Joint Size range Centre
distance
Flat Yes t = { 0.75 to 5
mm
No upper limit
Round Yes d = 3 to 20 mm No upper limit
V None b = 8 to 19 mm Limited
Timing None p = 2 mm and
up
Limited
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The characteristics of belts are:
They may be used for long centre distances. Except for timing belts, there is some slip and
creep, and so the angular-velocity ratio
between the driving and driven shafts isneither constant nor exactly equal to the ratio
of the pulley diameters.
In some cases an idler or tension pulley can
be used to avoid adjustments in centredistance that are ordinarily necessitated by
age or the installation of new belts.
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(b) Crossed belt
(a) Open belt
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(a) Non-reversing open belt
(b) reversing belt drive
(c) reversing open-belt drive
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Quarter-twist belt
drive; an idler guide
pulley must be used if
motion is to be in both
directions
This drive eliminates the
need for a clutch. Flat belt
can be shifted left or right
by use of a fork.
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Variable speed belt drives
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Flat and Round-Belt Drives
Modern flat-belt drives consist of a strong elastic
core surrounded by an elastomer; these drives
have distinct advantages over gear drives or V -
belt drives.
A flat-belt drive has an efficiency of about 98percent, which is about the same as for a gear
drive. On the other hand, the efficiency of a V-belt
drive ranges from about 70 to 96 percent.
Flat-belt drives produce very little noise andabsorb more torsional vibration from the system
than either V-belt or gear drives.
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The contact anglesCdDd
2sin2 1
C
dD
D 2sin2 1
where D= diameter of large pulley
d= diameter of small pulley
C = center distance= angle of contact
The length of the belt
L = [4C2
- (D - d)2
]1
/2
+1/2(DD + dd)
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For these the angle of wrap is the same for both
pulleys and is
= + 2 sin-1C
dD
2
The belt length for crossed belts is found to be
L = [4C2 - (D + d)2]1/2 + /2(D + d)
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Figure 9.6
Free-body of an
infinitesimal element
of a flat belt in
contact with a pulley d F
F + dF
dN
fdN
dS
dS due to centrifugal forcedN - normal force between the belt and pulleyf dN - shearing traction due to friction at the point of slipbelt width bthickness t
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Belt speed,
1000
dnV
m/sec
The weight of
meter of belt 6
10
bt N/m
where = weight density (N/m3)
Hoop tension due to centrifugal force,
Nv
Vg
Fc81.9
)(2
2
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whereFi = initial tensionF = tension due to the transmitted torque TD = diameter of the pulley
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F1 F2 = 2T / D = T / D/2
ci FFFF
2
21
1)exp(1)exp(
ff
DTFi
1)exp(
)exp(2
f
fFFF ici (F1)a = b Fa Cp Cv
where (F1)a = allowable largest tension, Nb = belt width, mmFa =manufacturers allowed tension,
N/mm or N/mCp = pulley correction factorCv
= velocity correction factor
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The Steps in Analysing a Flat-Belt Drive
1. Find exp(f) from belt-drive geometry and friction2. From belt geometry and speed find Fc3. From Nm find necessary torque
4. From torque T find necessary (F1)aF2= 2T/D5. Find F2 from (F1)a[(F1)aF2]
6. From eq. find necessary initial tension Fi
7. Check the friction development, f< f. Solve forf:
8. Find the factor of safety from fos = Ha/(HnomKs)
n
nHKT ds
159
ci FFF
F
2
21
c
ca
FF
FFf
2
1)(ln1
'
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Chains
A chain drive consists of endless chain wrappedaround two sprockets
The chain consists of a number of links connected by
pin joints, while the sprockets are toothed wheels with
a special profile of teeth.
The chain drive is intermediate between belt and geardrives. It has so some features of belt drives and
some of gear drives.
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The Advantages of Chains
Cost effectiveness and economy of chains and sprockets.
Large speed ratios;
Sufficient elasticity to absorb reasonable shocks;
A constant speed ratio between the driving and driven shaft;
Long life without excessive maintenance; Mechanical understandability regarding installation and
functionality;
Coupling and uncoupling with simple tools; and
A simple means to get power from its source to the location where
needed.
Th A li i f Ch i d i
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The Application of Chain drives
Chain drives are popular in the transportation industry, such as
bicycles, motor cycles and automobile vehicles. They are used in
metal and wood working machinery for the transmission ofpower. They are used in textile, building construction and
materials handling machinery.
Drive Design
The steps to design the drive as follows:
Selection of the chain and sprocket sizes.
Determination of chain length, center distance, method of
lubrication, and in some cases the arrangement of chain casingsand idlers.
Chain and sprocket selection is based on the
horsepower and type of drive;
the speeds and sizes of the shafting;
the surrounding conditions.