1.2 PRIMARY MACHINE ELEMENTS
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The various elements of textile machines such
as openers, condenser, material transport fans, lickerin, cylinder,
doffer, lap rollers etc are mounted on shafts. Gears, pulleys of belt
drives, sprockets of chain drives are always mounted on shafts. The
shafts must be supported physically in place and rotate with least
friction. To achieve these, shafts are supported by stationary machine
elements ‘bearings’. Further, many transmission shafts (main and
auxiliary) are used on textile machines to transfer motion from one
element to other. Drafting rollers, feed rollers, detaching rollers,
spindles, flyers and crank shafts act as transmission shafts and also do
their intended function(s). These are also mounted on bearings. In fact
there is no machine without shafts and bearings. Hence, the shafts and
bearings are called ‘primary elements’. The shafts and drafting rollers
must have adequate strength to overcome various stresses (shear,
bending, compression and torsion). The design aspects of these are
covered in module 8. The module 11 deals with bearings
that include the fundamentals of lubrication in bearings, bush
bearings, various types of rolling contact bearings, applications in
textile machines and comparison of bearings.
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1.3 SPECIAL PURPOSE DRIVES
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Apart
from the above mentioned general purpose drives and primary machine
elements; there are special requirements such as reversing drives to
change the direction of rotation of driven element with respect to the
driver element using flat belt, variable speed devices using conical
pulleys/disks and stepped pulleys, and drives to drive an element which
is out of plane with the driver. The principles used in these drives and
their applications in textile machines are discussed in module 2.
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Precise
control of bobbins in roving machine, detaching rollers in comber and
feed roller in lap forming are very important. A class of gear train
called ‘epicyclic gear train’ or ‘planetary gears’ are used to combine a
fixed and a variable speed to get an output speed that control the
speed of bobbins and detaching rollers. These are discussed in module 6.
In the case of roving and lap forming machines, the cone pulleys are
used to get the variable input speeds. In this respect, the designs of
cone pulleys are important. The design aspects of straight and profiled
cone pulleys are covered in details in module 7. The roles of belt slippage and bobbin diameters are also dealt in this module.
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1.4 DEVICES
A
clutch is used to safeguard the electric motor during starting of the
machine. During starting of a machine, all the elements of the machine
are static and hence the load requirement on the motor is very high.
This may result in burning of coils in the armature of the motor. A
clutch acts as an interface between the motor and machine. Usually the
clutch is disengaged as the motor is started so that the power is not
transmitted to the machine. Once the motor attains enough speed and
torque, the clutch is engaged transferring power from motor to the
machine. Apart from this universal application of clutches in heavy
industrial machines (including textile machines), clutches are used for
specific purposes to transfer or discontinue power transmission to
certain elements depending on the process requirements. Delayed start of
drafting rollers on ring spinning machines, control of feed apron on
bale opener, lap roller on sliver doubling machine, yarn under winding
on ring spinning, traverse motion of bobbin rail on roving machines and
fabric roll up mechanism on loom are controlled by clutches. Brakes are
used to stop a machine element or the whole machine or to compress
materials (lap formation). The clutches and brakes are invariably used
together on the main drive of heavy machines. For example, when a
machine has to be stopped, clutch must be disengaged followed by braking
action as in automobiles. The principles, construction and working of
clutches such as jaw, disk (single and multiple), cone, and centrifugal
clutches and their applications in textile machines are discussed in module 9.
Similarly, the block, band, disk brakes, and disk clutch-and-disk brake
and their applications on lap former, ring spindle, warping machine,
and negative let-off warp on looms are discussed in module 10.
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Cams
are used in many textile machines to preciously control the speed of
various elements. The classification of cams, and design aspects of cam
used to build ring cop of required profile are discussed in module 12.
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Finally,
balancing of machine elements and whole machine is an important issue
for good running performance of machines and product quality. Unbalance
is the unequal mass distribution of rotor (shaft having pulleys, gears
etc) about its axis. This causes vibrations on machines, especially at
high speeds which lead to noise, structural damage to parts/machine,
maintenance problems, poor product quality and reduced bearing life. The
module 13 is concerned with balancing machines. The causes and effect
of unbalance, perception/visualization of unbalance, various types of
unbalance, balancing of card cylinder, practical aspects of unbalance
during maintenance activities, practical examples of unbalance on
textile rotors and how were they balanced, effect of eccentricity in
mounting the shaft in bearings, and dynamic balancing of single and
multi-plane rotors are discussed in this module.
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| 2.1 DRIVES IN MACHINES |
Belt
drives such as flat belt, V belt, round belt, timing belt and tape
(thin belt made from cloth and composite) are widely used in textile
machines. They are simple and inexpensive compared to gears drives. Belt
drive requires an endless belt and two pulleys (a driver and driven).
Mostly they are used to transmit power between two parallel shafts by
means of friction. The belt must be set with some initial tension to
avoid it slipping over the pulleys for effective power transmission.
Depending on the cross-sectional shape of belts, they are classified as
flat, V and round belts.
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Belt
drives offer maximum versatility as power transmission elements. The
designer has considerable flexibility in choosing the location of
pulleys for the driver and driven. They are used for power transmission
over comparatively long distances. The design tolerances for these
drives are not as critical compared with gear drives. In many cases,
their use simplifies the design of machine and substantially reduces the
cost.
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The
advantage with belt drives is that they reduce vibration and shock
transmission, since the belts are elastic and usually quite long. These
properties play an important part in absorbing shock loads and isolating
the effects of vibration. This aspect is very important for the life of
machine. The belt drives are relatively quiet. The movement of belt
depends on friction traction on the pulleys and hence, some slippage is
inherent in their operation. The slippage of belt over the pulleys is
also responsible to absorb shocks and vibrations.
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Some
slip and creep are inherent in flat and v-belts, and so the angular
velocity ratio between the driver and driven is neither constant nor
equal to the ratio of the pulley diameters. Due to ageing or creep of
belts, in some cases, an idler or tension pulley must be used to avoid
the adjustments in center distance between the driver and driven
pulleys. The belts with excessive creep must be replaced with new belts.
Periodic inspection of belt slackness is required. Belts do not have an
indefinite life. While in use, it is essential to have regular
inspection schedule to guard against wear, ageing and loss of elasticity
due to creep, so that they can be replaced at the first sight of
deterioration.
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2.2
FLAT BELT DRIVE
Flat belts have narrow
rectangular cross-section. In fact the earliest belt used in industrial
drives was leather flat belt. Larger flat belt drives were in use as
group-drive system in industry decades ago. A large motor drives several
machines through pulleys and leather belts. Later, reinforced flat
flats were introduced which have almost replaced the leather belts due
to their superior characteristics. The important material properties to
be considered for the construction of flat belts are high coefficient of
friction between the belt and the rim of the pulleys, flexibility,
durability and strength of the belt.
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Leather belts
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Leather
belts were widely used earlier. Leather belts offer moderate coefficient
of friction between the rim of the pulley and belt. But they become
rigid, and exhibit creep over a period of time. They also have poor
resistance against moisture. The leather belts are available in two
varieties, viz., oak-tanned and mineral or chrome-tanned. Few layers of
leathers are bonded together by adhesives to get the required thickness
of belt. Commercial leather belts are specified according to the number
of layers, such as single, two, three and four-ply belts. A three-ply
leather belt is shown in Fig. 2.2.1.
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Fig. 2.2.1 Three-ply leather flat-belt
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Reinforced belt
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Another
category of flat belts is the reinforced belts, which are widely used
nowadays. The reinforced belts are made of urethane or rubber matrix,
reinforced with fabric or nylon cords or steel wires. In the case of
fabric reinforced rubber belts, canvas- or cotton-ducks fabrics are
used. Rubber impregnated fabric belts are cheaper, have more resistant
to moisture than leather belts. Either one or both the surfaces of belt
(the later is used in reversing drives, discussed in section 2.8)
require friction surface coating. Flat belts are quite, efficient at
high speeds, and can transmit large amounts of power over long
distances. They are mostly available in roll form and are cut into
required length, the cut ends are joined using special kits.
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The
coefficients of friction of leather, polyamide and urethane flat belt
are 0.4, 0.5 to 0.8 and 0.7 respectively. The reinforced belts are
available with a density of 0.97 to 1.29 g/cm3. The thickness of flat belts ranges from 0.75 to 5 mm. There is no upper limit on the length of flat belt to be used.
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Pulleys for flat belt
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The
pulleys used for flat belt are crowned to keep the belts from running
off the pulleys. Both the driver and driven pulleys must be crowned when
the pulley axes are not in a horizontal position. The crowns should be
rounded and not angled. If only one pulley is to be crowned, then it
should be the larger one.
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2.3 ANALYSIS OF FLAT BELT TENSIONS
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Fig. 2.3.1 Forces acting on an element of a flat-belt
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The normal force ( dN) acting on the belt arises due to reaction from the pulley. The coefficient of friction between pulley and belt is ‘ μ’. Due to friction traction, the belt tensions on both the sides of the element are F1 (on loose side) and F2 (on tight side), such that F2 > F1 and the friction force dF is equal to difference between these two forces. The angle of wrap of belt over the pulley is  (in radians). If a belt having a linear density of m (in kg/m) running over a rim of pulley at a velocity, v (in m/s), the element of belt shown in figure would be subjected centrifugal force equal to  (in N) |
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The above equation indicates that power transmission is proportional to
belt speed. However, at very high belt speeds (usually above 1500
m/min), power decreases with increasing belt speed due to rapid rise of
centrifugal force acting the belt. This centrifugal force reduces the
pressure between the belt and the rim of the pulleys, moving the belt
away from the pulley, reducing the wrap angle and hence, the belt
tensions and power transmission.
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2.4 POSITIONS OF SLACK AND TIGHT SIDES OF BELT
While the belt is running, the belt tension is such that ‘sag’ or
‘droop’ is visible on one side of the driving pulley. This is shown in
Fig. 2.4.1for flat belt drive.
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Click on Image to run the animation
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Fig. 2.4.1 Open belt drive with slack side on top of pulleys
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Animation: 2.4.1 Moving open belt with slack side on top of pulleys
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The positions of input and output pulleys are
such that the tight side of the belt must be on the bottom and slack
side on the top of the pulleys. Otherwise, the angle of contact between
the belt and rim of the pulley reduces, decreasing the power
transmission capacity of the belt.
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2.5 MAXIMIZING THE POWER TRANSMISSION
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| 2.6 GEOMETRICAL RELATIOSHIPS IN BELT DRIVES |
Flat belts are used in open and crossed configurations. A crossed belt is shown in Fig. 2.6.1. The geometry of open flat belt and crossed flat belt drives are shown in Fig. 2.6.2.
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Fig. 2.6.1 Crossed belt on a high speed card
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Fig. 2.6.2 Geometry of flat-belt drives: Top-Open belt; Bottom- Crossed belt
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| The contact angles (in degrees) of open belt over the smaller (driver) and larger (driven) pulleys (Fig. 2.6.2) are given below: |
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2.7 SELECTION OF BELT AND PULLEY DIAMETER
The machinery manufacturer has to select a
belt from the belt manufacture’s catalogue based on the power to be
transmitted, speeds and diameters of driving and driven pulleys and the
available space to house the pulleys. In order to give factor of safety
to the belt, the actual power to be transmitted by the belt is
multiplied by load correction factor to arrive at maximum power
transmission.
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The correction factor is one for a normal load and goes up to 1.5 when
the nature of load is shock with increasing intensity. From the pulley
manufacturer’s catalogue, a pulley whose size is nearest to the
dimension as per the design calculation has to be selected. As a
consequence the belt velocity and the size of the driven pulley would
also vary slightly.
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2.8 REVERSING DRIVES WITH FLAT BELTS
Reversing
drives (open or crossed) are used when the direction of rotation of
driven must be opposite to that of driver. This can be achieved by open
flat belt (Fig. 2.8.1) and crossed flat belt (Fig.2.8.2)
configurations. In these configurations, both the sides of belt contact
the pulleys. The V belts cannot be used for reversing drives. However, a
double sided timing belt can be used in an open configuration (Refer Fig. 2.17.2).
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Fig. 2.8.1 Reversing drives with open flat belt
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Fig. 2.8.2 Reversing drives with crossed flat belt
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2.9 FLAT BELT WITH OUT OF PLANE PULLEYS
Flat
belt drive could also be used when the pulleys are out-of-plane, which
is not possible with V belt drive. The driving and driven pulleys must
be positioned so that the belt leaves each pulley in the mid-plane of
the face of other pulley without using a guide pulley. This drive is
used to drive coiler plate on card as shown in Fig. 2.9.1.The schematic representation of the same is illustrated in Fig 2.9.2. For other arrangements guide pulleys are needed.
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Fig. 2.9.1 Flat belt on out-of-plane pulleys driving coiler on carding machine
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Fig. 2.9.2 Quarter-twist flat-belt drive (Pulleys are out-of-plane by 90°)
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| 2.10 CLUTCHING ACTION WITH FLAT BELT |
Clutching action can be obtained with flat
belts. The belt can be shifted from a loose to a fast (tight) pulley
mounted on the driven-shaft using a fork-lever or any other shifting
mechanisms as shown in Fig. 2.10.1.
This type of arrangement is very common on conventional blow rooms,
drawing and roving machines. While starting the motor, the belt is
placed on the loose pulley, which disconnects the motor from machine,
thus, preventing transfer of heavy loads on the motor. When the motor
attains full speed, the drive is transferred to the machine by shifting
the belt on to the fast pulley. Clutching device based on loose and fast
pulleys used on a old carding machine is shown in Fig. 2.10.2.
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Fig. 2.10.1 Flat belt on fast and loose pulleys
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Animation 2.10.1 Flat belt driving fast and loose pulleys
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Fig. 2.10.1 (b) Flat belt on fast and loose pulleys mounted on cylinder shaft of a card
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2.11 APPLICATIONS OF FLAT BELTS
Some of the applications of flat belts are given below:
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Drives to beaters on conventional blow rooms.
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Crossed flat-belt transmits drives from cylinder to flat on old cards.
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Drives
in high production cards such as the drive from motor to lickerin and
cylinder; drive to cleaner roller at the delivery side; drive from motor
to flat-stripper roller and crossed-flat-belt drive from cylinder to a
pulley from where further drive proceeds through double stage speed
reduction using worm and worm gears and a mechanical clutch to the
driving-shaft of flat.
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Drive to drafting rollers and other rolling elements on a single delivery drawing machine.
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Drives to opening rollers, friction drums and take-off rollers on friction spinning machine.
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Drive to rotor on rotor-spinning machine.
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Main drive on draw-texturing machine.
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Drive to creel-rollers of a high speed drawing machine.
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2.12 V BELT DRIVES
The V belts are the probably the most common means of transmitting power between fractional horse power motors to machines (Fig 2.12.1).
Mostly, the driver and driven pulleys lie in the same vertical plane.
There is an upper limit on the center distance or belt length. Long
center distances are not recommended, because the excessive vibration of
slack side flutters and shorten the belt life. In general the center
distance should not be greater than 3 times the sum of diameters of
input and output pulleys. Since the V belt is short, it is subjected to
the action of load and fatigue a greater number of times. Further, its
ability in absorbing the shocks is poor.
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Fig. 2.12.1 (a) V belt drive on a laboratory model card
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Fig. 2.12.1 (b) V belt drive on a loom
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Fig. 2.12.1 (c) V belt drive on a roving machine
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The
V belts work better in the speed range 300 to 1500 m/min. V-belts are
widely used in variable speed drives using adjustable sheaves. By moving
the sheaves axially the pitch diameters of the driving and driven
pulleys could be varied to get variable output speed. This type of drive
is common on ring spinning and rotor spinning machines. Quarter-turn
drives are used to transmit motion between horizontal and vertical
shafts using deep groove pulleys and relatively long center distances.
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2.13 CONSTRUCTION OF V BELT
V belts are available without any joints. The cross-section of V belt is trapezoidal (shown in Fig. 2.13.1
). V beltsare designed to mesh in the trapezium shaped groove of pulleys. The groove angle (β)
of the sheave is made somewhat less than the belt-section angle (θ).
This causes the belt to wedge itself into the groove, thus increases the
friction. This increases greatly the frictional resistance to slipping,
for a given maximum tension, compared to flat belt. The V belt does not
rest on the bottom of the groove but wedges itself into the groove.
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Fig. 2.13.1 Geometry of a V belt
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The thickness ‘b’ ranges about 8 to 23 mm and the width ‘a’ is about 13
to 38 mm. The belt section angle is generally around 40° . The V belts
are available in sections as A, B, C, D, E. The width and thickness of
belt and minimum sheave diameter increase from section A to E, in other
words, belts become heavier from section A to E. To select a V belt for
different speeds and power transmission combination, one must refer to
belt manufacturer’s catalogue. For high power transmission, heavy V
belts are preferable. For high speeds, light belts are preferred.
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V
belts are made of fabric and cords which are moulded in rubber. It
consists of three elements, viz., a central load carrying layer of cords
made from high tenacity fibre or steel, a surrounding layer of rubber
to transmit pressure from cords to side walls and an elastic outer cover
to provide friction as shown in
Fig. 2.13.2.
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Fig. 2.13.2 Cross-section of a V belt
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2.14 FORCE ANALYSIS IN V BELT
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Fig. 2.14.1 Forces on a V belt
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2.15 APPLICATIONS OF V BELTS
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Main drives (drive from
motor) in all spinning, yarn preparatory, texturing machines, looms,
warping and winding machines and compressors.
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Drive from top coiler to base coiler plate of high speed carding machine.
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2.16 ROUND BELTS
The round belts are circular in cross-section, without any joints. They
can be used for transmission over a long distance. The pulleys on which
it runs should have V-shaped groove, similar to the ones used for V
belts. This belt could also be used for variable speed drives using
stepped pulleys. When all the pulleys (driving, driven and guide
pulleys) are at considerable distances, and at different planes, these
belts are the ideal choice. One such example is the drive to grooved
winding drums on friction-spinning machine. The drive to winding drum on
a friction-spinning machine is shown in Fig. 2.16.1 and the schematic representation of the same is shown in Fig. 2.16.2.
The motion is transmitted from a pulley, ‘A” to pulley, ‘B’ through
guide pulleys, ‘C’ & ‘D’. From the pulley, ‘B’ drive is transmitted
to a grooved winding drum (not shown in the picture).
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Fig. 2.16.1 Round belt drive on friction spinning machine
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Fig. 2.16.2 Line sketch of round belt drive on friction spinning machine
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2.17 TOOTHED BELT DRIVES
They
are also referred as ‘timing belt drives’. They are positive drives
that operate on toothed pulleys. The belts have flat outer surface and
evenly spaced teeth on the inner surface. A toothed belt is made of
rubberized fabric reinforced with steel wires to take the load. The
steel wire is located at the pitch line and the pitch length is the same
regardless of the thickness of belt. Toothed belts do not have joints.
The toothed pulley looks like a spur gear (shown in Fig. 2.17.1), but the tooth profile is not involute.
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Fig. 2.17.1 Timing-belt drive
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Characteristics of toothed belt drive
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Toothed
belts offer very good accuracy in transmitting motion compared to flat
belts and are comparable to gears. In addition they offer greater
flexibility in the location of driver and driven. The tensions on timing
belts are low, consequently the load on the supporting bearing are also
low.
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They are commonly used on high-speed
machines, when the distance between driver and driven is considerably
long. In these situations they offer greater advantage over gear drives
in terms of lower power consumption and noise. In the case of gear
drive, train of gears is required with several carrier gears, which,
leads to high power consumption and more noise. In addition, the gear
drive becomes so complex that changing the gears to alter process
parameters or removing and refitting the gears during maintenance
operation would be cumbersome.
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Toothed belt do not stretch or slip much,
consequently transmits power at constant angular velocity. Timing belts
do not require high initial tension required for the flat and V belts.
They operate over a wide range of speeds, with efficiencies in the range
of 97 to 99%. They are quieter than chain drives. There is no periodic
speed variation, as with chain drives, and so they are an attractive
solution for precision-drive requirements. There is an upper limit on
the maximum center distance between the wheels, which is lower compared
to the flat belts.
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Applications of toothed belts
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Toothed belts are used on
texturing machines and to drive doffer, stripper, calender and coiler
rollers (double sided toothed belt) on high speed card, and coiler
plates of combing machine. In new drawing and ring spinning machines the
drafting rollers are driven by toothed belt drives. The phenomenon of
fluctuating speeds with gear drives due to accumulation of fibres/dust
on gear teeth, wearing teeth, and improper meshing of gears by
deflection of shaft or misalignment of gears are eliminated with the use
of timing belt drives. In looms, toothed belt drives are used to drive
take-up roller, dobby/tappet shaft and warp let-off motion. Toothed belt
drives used on an air-jet texturing machine and card are shown in Fig. 2.17.2.
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Fig. 2.17.2 Timing belt drive on air-jet texturing and carding machines
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The
driving and driven wheels have discs on their sides to prevent belt
coming out, in case the wheels are misaligned. The belt is kept under
tension by means of a tension wheel (Fig 2.17.3),
which does not have side discs. This helps in sliding the belt over the
tension pulley after changing the driver or driven pulleys.
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Fig. 2.17.3 Tension wheel on a timing belt drive
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The
driving and driven wheels have discs on their sides to prevent belt
coming out, in case the wheels are misaligned. The belt is kept under
tension by means of a tension wheel, which does not have side discs.
This helps in sliding the belt over the tension pulley after changing
the driver or driven pulleys.
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2.18 TAPES
Tapes are very thin and highly flexible compared to flat belts. They
are generally made from narrow woven fabrics. Tapes are very useful to
drive a group of elements from a single source, following very tortuous
paths. They can easily follow sharp curved paths, and bend and twist
over the supporting or tension compensating pulleys. Tapes are used in
‘Four spindle group drive system’ to drive spindles on ring spinning
machines (shown in Fig. 2.18.1
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Fig. 2.18.1 Four-spindle group-drive system with tape
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Each tape moves over a tin roller or jockey pulley of driving shaft and
tension pulleys to drive a set of four spindles. The spindle wharves are
crowned. Thin flat belts are also used as ‘Tangential drive’ to drive
spindles.
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2.19 VARIABLE SPEED DRIVES
Cone and stepped pulleys
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For variable speed drives in blow rooms and roving machines, flat belts with cone pulleys are used as shown in Fig 2.19.1.
The belt is moved axially to vary the output speed. For stepped
pulleys, V belt or round belt is used with grooved sheaves as shown in Fig. 2.19.2. The stepped pulleys with V belts are commonly used on many main drives of textile machines.
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Click on Image to run the animation
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Animation 2.19.1 Variable speed using cone pulleys
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Fig. 2.19.1 Variable speed drive with cone pulleys
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Click on Image to run the animation
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Animation 2.19.2 Variable speeds with stepped pulleys
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Fig. 2.19.2 Variable speed drive with stepped pulleys
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A variable speed drive
using adjustable grooves/conical discs and V belt are commonly used in
ring spinning without varying the speed of the motor as shown in Fig. 2.19.3 and Fig. 2.19.4.
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Fig. 2.19.3 Speed variation using conical discs on ring spinning machine
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Click on Image to run the animation
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Animation 2.19.4 Speed variations with conical discs
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Fig. 2.19.4 Speed control on ring spinning using conical discs
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By shifting the driver and driven discs
axially and simultaneously, the effective diameters of the discs over
which the belt passes are varied, thus varying the output speed. To
increase the output speed (spindle speed), the input discs are moved
closer to each other and the output discs are moved apart and vice
versa. A microprocessor controls the hydraulic or pneumatic piston and
lever mechanism to moves the discs. Depending on the preciousness of the
control mechanism, the speed of the output can be varied
infinitesimally and continuously. This is called PIV (Positively
Infinitesimally Variable) drive. However, the spindle speed in ring
spinning is not continuously varied. In practice, the spindle speed is
varied in several steps depending on the doff-position and the
permissible end-breakage rate of yarn. This permits higher throughput of
yarn as optimum spindle speed could be selected at any instant. To
reduce slip even further, the V-belts are replaced by a set of steel
links held together by means of a chain (slated chains). This is called
PIV gear and is used in many industrial machines for speed control.
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| 2.20 ADJUSTMENT OF BELT TENSIONS |
Belts become slack due to creep during its
service life. Therefore, a provision should be made to adjust the belt
tension from time to time. Different methods are available to adjust
belt tensions. In the case of flat belts with joints or hinges, a short
length of belt is cut periodically and the cut ends are joined back to
remove the slackness in the belts.
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Movable and swinging motors
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For endless belts such
as V belts and some flat belts, the technique of cutting the belt to
adjust belt tension is not possible. In such cases, the center distance
between input and output pulleys is slightly increased by means of an
adjusting screw. On the drive from motor to main shaft of machine,
provision is made to move the motor away from the output pulley through
adjusting screws on the motor platform as shown in
Fig. 2.20.1.
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Fig. 2.20.1 (a) Motor mounted on movable flat bed on a loom
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Fig. 2.20.1 (b) Motor mounted on movable flat bed
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Another way of adjusting the belt tension is
to mount the motor on a swinging platform/hanging plate, called
‘Rockwood belt drive’ or ‘Pivoted motor’ used in bale opener is shown in
Fig. 2.20.2. This type of drive is
used in bale opener to drive the take-off and evener rollers. The motor
is mounted on an over-hang-plate.
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Fig. 2.20.2 Swing motor drives on Bale opener
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In pivoted motor drive, the belt length is adjusted automatically, when the distance ‘z’ of the center of gravity of motor from the pivot changes due to creep on the belt (Fig. 2.20.3). Hence, the belt tension is also adjusted. Taking moments of forces at the pivot,
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Fig. 2.20.3 Forces acting on a pivoted motor drive
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In this drive, the belt length is adjusted automatically, when the distance ‘z’
of the center of gravity of motor from the pivot changes due to creep
on the belt. Hence, the belt tension is also adjusted. Taking moments of
forces at the pivot,
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| Idler or tension pulley |
Adjustment of belt tension can also be carried out using an idler pulley. This idler pulley may be either spring-loaded ( Fig. 2.20.4) or held against the belt by its own weight (Fig. 2.20.5) or by external adjustable tensioning arrangement (Fig. 2.20.6).
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Fig. 2.20.4 Spring loaded idler pulley on friction spinning machine
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Fig. 2.20.5 Weighted idler pulley
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In
all the cases, the idler pulley should be located next to driver pulley
on the loose side of belt. The contacting face of the idler pulley is
flat faced without any crown. The idler pulley increases the arc of
contact between belt and driver pulley, which is also advantageous in
drives with short center distance.
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A flat-belt drives lickerin and cylinder through adjustable tension pulley on a high speed carding machine ( Fig. 2.20.6).
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Fig. 2.20.6 Flat belt drive to lickerin and cylinder with tension pulley
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A tension pulley is placed on the loose side
of belt close to the motor pulley. The tension pulley is mounted on a
slot fixed to the machine frame. Belt tension is adjusted by moving the
tension pulley through the slot. When the machine is not operated for
long period, the tension on the belt can be released to avoid
unnecessary creep on the belt and to improve the service life of belt.
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2.21 COMPARISON OF FLAT AND V BELTS
The advantages of flat belts in compared to V belts are listed below:
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The tapes are very simple
in design and cheapest followed by flat belts. The complexity of
construction and cost are higher with round belts, V-belts and timing
belts. The timing belts are the most expensive due their complex
designs.
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The periodic adjustment of belt tension and replacement of belts when worn out are easier in the case of tapes and flat belts.
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Precise alignment of pulleys and shafts are not so critical with tapes and flat belts.
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Flat belts and spindle
tapes are flexible and long, they have better ability to absorb shock
and torsional vibrations. Hence, they are quieter and also give better
protection to the machinery against impact or overloads compared to
other belt drives.
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Clutching action using
fast and loose pulleys and variable speed drive with flat belts are
possible whereas these are not possible with other belt drives.
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Flat belts can be used for
long distances, even up to 15 m, where other types of drives cannot be
used. V-belts, timing belts and tapes are used for short distance.
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The construction of
V-grooved pulleys used for V-belt and round belt drives is complicated
and costlier compared with the pulleys used for flat belt.
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Tapes are very thin and
highly flexible and hence have the ability to bend and twist over
pulleys and follow very tortuous paths. They are most suitable for
spindle drives, whereas others cannot be used for driving spindles.
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The timing belts have very
higher power transmission capacity than other belt drives due to their
strength and positive grip provided by the toothed cross-sections of
belt and wheels. The V-belts have higher power transmission capacity
than flat belts, round belts and tapes. The wedging action between the
V-belt and V-pulleys permits small arc of contact that increases the
power transmission capacity and reduces belt slip to a greater extent.
The V-belt tends to wedge into the groove when the load increases,
transmitting more torque. Tapes are the weakest and can be used for
transmitting extremely low loads.
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The creep in tapes, V-belts and round belts are higher compared to timing belt and flat belts.
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The V-belts, round belts
and timing belts are made in endless form, which results in smooth and
quit operation even at high speeds. Few reinforced flat belts are also
made in endless form.
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V-belt drives can be used
for speed reduction up to 7:1 and they can be operated even the belt is
vertical. They require less width and suited for smaller centre distance
compared to flat belts. For high power transmission, two or more
V-belts running on pulleys having multiple grooves can be used. The main
drives (motor to main shaft of machine) in textile machines have the
characteristics of high speed ratio, smaller centre distance, leading to
smaller angle of contact (<180 action="" and="" are="" div="" driver="" drives="" for="" friction="" hence="" in="" is="" less="" machines="" main="" majority="" much="" of="" on="" power="" pulley="" situation.="" so="" textile="" the="" this="" traction="" transmission.="" useful="" v-belt.="" v-belt="" wedging="">
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The ratio of bending force
acting on the shaft to the net force is 1.0 for timing belt, 1.5 for V
belt, whereas it is 2 for the flat belt. This implies that for a given
power transmission (product of torque and speed), timing belt drive
requires a smallest (diameter) shaft and the flat belt drive requires a
largest shaft.
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The ratio of thickness of V
belts to pulley diameter is high, which increases the bending stress in
the belt cross-section and adversely affects its durability.
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3.1 INTRODUCTION
A chain drive consists of an endless chain wrapped around sprocket wheels (shown in Fig. 3.1.1).
The chain has a number of links connected by pins. The sprockets have
teeth of special profile. Chains are used for power transmission and as
conveyors. The chain drives have some features of both belt (flexibility
of location of driver and driven) and gear drives (ruggedness). Chain
drives are recommended for velocity ratio below 10:1, chain velocity
1550 m/min and power transmission up to 100 kW.
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3.2 CONSTRUCTION OF ROLLER CHAIN
Roller chain is made up of alternate link plates (inner and outer), pins, bushes and rollers as shown in
Fig. 3.2.1.
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Fig. 3.2.1 Construction of a roller chain
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The pins, bushes and rollers are made of alloy
steels. The pins are press fitted to the outer link plates. The bushes
are press fitted to two inner link-plates. The bush and the pin form a
swivel joint and the outer link is free to swivel with respect to the
inner link. The rollers are loosely mounted on the bushes so that they
rotate when they are engaged with the teeth of the sprocket wheels. This
results in rolling friction between the roller and sprocket teeth,
reduces friction and results in less wear on them. The pitch of the
chain ‘p’ is measured between the axes of adjacent rollers. The width of the chain (b1) is defined as the space between the two inner link plates along the axis of the pin.
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3.3 CLASSIFICATION OF CHAINS
Chains are classified as roller chains and
silent chains (inverted tooth or side guide chains). Single roller chain
(or simple chain) drives are shown in Fig. 3.3.1. Figure 3.3.2
shows both the single and double roller (duplex) chains. The
construction of single roller chain is already explained in the earlier
section. A duplex roller chain can be visualized as having two single
roller chains placed side by side mounted on same set of pins. The
silent chains are heavier, more difficult to manufacture and expensive
compared to roller chains, hence their applications are limited.
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Fig. 3.3.1 Single roller or simple chain on bale opener
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Fig. 3.3.2 Simple and duplex roller chains on opening and cleaning machine
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3.4 LUBRICATION OF ROLLER CHAINS
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Roller chains must be lubricated to achieve long and trouble-free life.
A drop-feed lubrication or lubricant in a shallow bath can be used. A
medium or light mineral oil, without additives can be used as
lubricants. Heavy duty oils and greases which are highly viscous do not
enter the small spaces in the chain parts; and hence they are generally
not recommended.
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3.5 CHAIN TENSION AND BENDING FORCE ON SHAFT
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Fig. 3.5.1
shows a pair of chain sprockets transmitting power. The upper part of
the chain is in tension and produces the torque on either sprocket. The
lower part of the chain is slack and exerts no force on either sprocket.
Therefore the total bending force on the shaft carrying the sprocket is
equal to the tension on the tight side of chain.
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Fig. 3.5.1 Forces acting on chain sprockets
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| 3.6 GEOMETRICAL RELATIONSHIPS IN CHAIN DRIVE |
Fig. 3.6.1 shows a sprocket rotating in counterclockwise direction drives a chain. The symbols p, γ , d and z denote for the pitch, pitch angle and pitch diameter and number of teeth on the sprocket respectively.
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Fig. 3.6.1 Geometry of a chain drive
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3.9 APPLICATIONS OF ROLLER CHAINS
Few applications of roller chains are listed below:
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Pedal roller of scutcher.
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Drives from beater to plain and perforated drums and feed rollers on fine cleaner are through duplex roller chains.
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Drive from inclined lattice to feed apron and creel apron of bale opener through clutch.
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Motor to feed-roller, lap winding-roller, and tuft-feeder in high production carding machine.
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Duplex roller chain transmits motion from main shaft to lap rollers via bottom calender roller on sliver lap machine.
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Drive to shafts driving the flyers and bobbins on conventional roving machines.
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Drive to ring rail on ring spinning machines.
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Drive to creel rollers on drawing machines, and hank meters ( Fig. 3.9.1).
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Fig. 3.9.1 Chain drive for hank meter on drawing machine
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Drive to brush roller shaft on comber.
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Drive to drafting rollers that feed sheath fibres on friction spinning machine.
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A drive to creel or table rollers (C, E, G and H) of conventional drawing machine is shown in Fig. 3.9.2.
Initially, the drive originates from a driving sprocket, ‘A’ (behind
the back drafting roller) to a sprocket, ‘B’ mounted on the shaft of
first table roller through a tension sprocket wheel. The sprocket C
compounded with the sprocket B drives the sprocket D mounted on the
second table roller through a tension sprocket wheel (not shown in the
figure) and so on to other table rollers. In high speed drawing
machines, chains have been replaced by timing belts.
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Fig. 3.9.2 Drive to table rollers on a conventional drawing machine
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4.1 Introduction
Gears have specially constructed toothed profile and are extensively
used to transmit power in machines. Gears can be classified into spur
gears, helical gears, bevel and worm gears. Within these gears there are
sub-classification based on designs. Gears are made of ferrous (steel,
cast iron), non-ferrous metals (bronze based) and non-metallic materials
(Nylon, fibre reinforced in phenolic resin etc.). Steel is the most
widely used material for gears. Spur gears are the simplest gears,
having the maximum precision and high power transmission efficiency
compared to any other gears. Hence, they are preferred as the first
choice in industrial machines, except high speed and high load
applications. In spur gears, two meshing gears are mounted on parallel
shafts. The teeth are cut parallel to the axis of gear. In a normal or
external spur gear, the teeth are cut on the outside of the rim of gear ( Fig. 4.1.1).
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Fig. 4.1.1 Normal or external spur gears on ring spinning machine
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Generally, the input gear is smaller in size
and the output gear is larger in size to get speed reduction. The
driver and the driven gears are called ‘pinion’, and ‘gear’, respectively.
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4.2 DESIGN ASPECTS OF SPUR GEAR
Nomenclature of spur gear :
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The nomenclature of spur gear is illustrated in Fig.4.2.1.
The pitch circle shown in the figure will not be visible in an actual
gear; but the entire design of gear is based on the pitch circle
diameter or the pitch diameter. The pitch circles of a pair of meshing
gears must be tangent to each other. The circular pitch, p corresponds
to the distance, measured on the pitch circle, from a point on one tooth
to a corresponding point on an adjacent tooth. In other words, the
circular pitch is equal to the sum of the thickness of a tooth and the
space between two adjacent teeth measured along the pitch circle.
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Fig. 4.2.1 Terminology of spur gears
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The following notations are used in spur gears:
P = Diametral pitch
z = Number of teeth
d = Pitch circle diameter
m = Module (mm)
p = Circular pitch (mm)
a = Addendum
b = Dedendum
c = Clearance = b - a
do = Diameter of addendum circle or Outside diameter =(d + a)
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The module ‘m’ is the ratio of
the pitch diameter to the number of teeth on the gear. The unit of
module in SI system is mm. The diametral pitch P is the ratio
of the number of teeth on the gear to its pitch circle diameter. It is
the reciprocal of module. The diametral pitch is usually expressed as
‘teeth per inch’.
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The addendum circle (visible on a gear) is the largest circle on the gear. The addendum ‘a’
is the radial distance between the pitch circle and the addendum
circle. The dedendum circle (visible on a gear) is usually the smallest
circle on the gear. The dedendum ‘b’ is the radial distance between the pitch circle and the dedendum circle. The dedendum is larger than the addendum; i.e., b > a. The depth of tooth ‘h’ is the sum of the addendum and dedendum; i.e., h = (a + b).
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The base circle or clearance circle of a gear is tangent to the addendum circle of its meshing gear. The clearance ‘c’ is the difference between the dedendum (b) and addendum (a) of the gears.
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Geometrical relationships in spur gears :
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4.3 CONJUGATE ACTION
The gears must be designed such that the
ratio of rotational speeds of driven and driver gear is always constant.
When the tooth profiles of two meshing gears produce a constant angular
velocity during meshing, they are said to be executing conjugate
action. That is
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(ω1 / ω2 ) = constant. ................................................................(4.5)
Where ω1 = Angular velocity of the driver.
ω2 = Angular velocity of the driven.
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Gears are mostly designed to produce
conjugate action. Theoretically, it is possible to select an arbitrary
profile for one tooth and then to find a profile for the meshing tooth,
which will give conjugate action. One of these solutions is involute
profile. The involute profile is universally used for constructing gear
teeth with few exceptions. Figure 4.3.1 illustrates a conjugate action.
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Click on Image to run the animation
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Animation 4.3.1 Illustration of conjugate action
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Fig. 4.3.1 Principles of conjugate action
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4.4
GENERATION OF INVOLUTE ON A CYLINDER
To understand the involute properties, let us
consider a cylinder ‘A’, on which a flange ‘B’ is attached by a thread
‘xyz’ wrapped around the cylinder, and the cord is held tight ( Fig. 4.4.1).
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Click on Image to run the animation
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Animation 4.4.1 Illustration of involute generation on a cylinder
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Fig 4.4.1 Generation of involute on a cylinder
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Assume a marker is attached to the thread at a point ‘b’. While the
thread is wrapped and unwrapped around the cylinder (rotating the
cylinder in clockwise and anti-clockwise directions, keeping the thread
tight all the times), the movement of marker traces an involute curve
'abc' over the cylinder.
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The radius of curvature of involute varies continuously. It is zero at point 'a', (on the cylinder) and maximum at point 'c'(far away from the cylinder). At point 'b' the radius of involute is equal to the distance 'by', since the point 'b' is instantaneously rotating about the point 'y'
on cylinder. Thus the line ‘xby’ coinciding with the tracing arm of
thread ‘yb’ is normal to the involute at all points of intersection. The
line ‘xby’ is called the line of action. The line of action is always
tangent to the cylinder ‘A’ which is called ‘base circle’ on which the
involute is generated.
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4.5 INVOLUTE PROFILE OF GEAR TEETH
An example involute profile of gear teeth is shown in Fig. 4.5.1. Two gear-blanks A and B are centered about O1 and O2
respectively. Let us imagine that a cord ‘xy’ is attached to both the
base circles of these gears. When the base circles are rotated in
different directions keeping the cord always under tension, a point on
the cord will trace out two involute profiles, ‘cd’ on the base circle
of gear ‘A’ and ‘ef’ on the base circle of gear ‘B’. The involutes are
thus generated simultaneously by tracing the points.
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Fig. 4.5.1 Principles of generation of involute profile for gear teeth
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Each tracing point on the involutes represents
the point of contact between the involutes. The portion of cord ‘ab’ is
the generating line. The point of contact moves along the generating
line. The generating line is a fixed line, as it is always tangent to
the base circles which are fixed. It is clear that the generating line
is always normal to the involutes at the point of contact. Thus, the
requirement for constant angular velocity ratio is satisfied.
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4.6 CONSTRUCTION OF INVOLUTE GEAR TOOTH
The
procedure to construct a gear tooth having an involute profile is given
below. Construct a segment of base circle of the gear (centered at ‘O’)
. Divide the segment of the base circle into a number of equal parts
separated by very small angle ( q ). Construct radial lines OA4, OA3, OA2 etc as shown in
Fig. 4.6.1.
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 Click on Image to run the animation
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Animation 4.6.1 Illustration on construction of involute gear tooth
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Fig. 4.6.1 Construction of involute gear tooth
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Construct tangents to the circle A4B4, A3B3, A2B2, A1B1 and from A4, A3, A2 and A1 respectively. Then along the line A1B1, mark the arc-distance A1A0 from A1; along the line A2B2, mark the twice the arc-distance A1A0 from A2 and so on; to get the points B1’, B2’, B3’ and B4’ etc.
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The curve joining these points starting from A0, would an involute curve A0B1’B2’B3’B4’.
In a gear, the involute profile of the tooth starts from the base
circle and continues up to the addendum circle with continuously
increasing radius. In the procedure described above, the points A0,B1’, B2’, B3’, B4’ are discrete; whereas in actual gear teeth profiling, the θ is infinitesimal that continues points can be generated to get a perfect involute profile for the gear teeth.
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4.7 CONTACT RATIO
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Contact
ratio of gears is one of the important design aspects of spur gear.
This is a number, which indicates the average number of pairs of teeth
in contact. This is the ratio equal to the length of path of contact on
pitch circle divided by the circular pitch. Gears are generally designed
to have a contact ratio larger than 1.2, because any inaccuracies in
mounting the gears might reduce the contact ratio, increasing the
possibility of impact between the meshing teeth and consequently the
noise level.
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4.8 PRESSURE ANGLE
| Pressure angle (ø)
is the angle between the common normal to the contacting teeth (line of
action) and the common tangent to the pitch circles of meshing gears
(in Fig. 4.8.1). The relationship between radii of base (rb) and pitch circles (r) and the pressure angle (ø ) is: |
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Fig. 4.8.1 Pressure angle and radii of base and pitch circles
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| Pressure angle (ø)
is the angle between the common normal to the contacting teeth (line of
action) and the common tangent to the pitch circles of meshing gears
(in Fig. 4.8.1). The relationship between radii of base (rb) and pitch circles (r) and the pressure angle (ø ) is: |
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Fig. 4.8.1 Pressure angle and radii of base and pitch circles
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4.8 PRESSURE ANGLE
| Pressure angle (ø)
is the angle between the common normal to the contacting teeth (line of
action) and the common tangent to the pitch circles of meshing gears
(in Fig. 4.8.1). The relationship between radii of base (rb) and pitch circles (r) and the pressure angle (ø ) is: |
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Fig. 4.8.1 Pressure angle and radii of base and pitch circles
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| Pressure angle (ø) is the angle between the common normal
to the contacting teeth (line of action) and the common tangent to the
pitch circles of meshing gears (in Fig. 4.8.1). The relationship between radii of base (rb) and pitch circles (r) and the pressure angle (ø ) is: |
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Fig. 4.8.1 Pressure angle and radii of base and pitch circles
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4.9 INTERFERENCE IN GEARS
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If the contact portions of tooth profiles of
meshing gears are not involute, then the gears do not execute conjugate
action; that is the output gear will not have constant angular
velocity. This is called ‘interference’. In Fig. 4.9.1, two meshing gears are shown. The initial and final points of contact are at ‘A’ and ‘B’, respectively.
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Click on Image to run the animation
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Animation 4.9.1 Illustration of interference on gears
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Fig. 4.9.1 Gears with interference
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The explanation of interference is given
below. In this figure, the initial contact begins between the teeth of
meshing gears at point ‘A’. This indicates the contact begins when the
tip of the tooth of driven gear contacts the flank of driving tooth
below the base circle of driving gear on the non-involute portion of the
tooth of driver. If the contact begins only at ‘C’ on the involute
portion of tooth of driver, then there is no interference. Similarly,
the contact should end at point ‘D’, just on the pressure line. If the
contact ends at ‘B’, the effect is for the tip of the driver tooth (an
involute portion) to dig out the non-involute portion of driven tooth,
i.e. above the pressure line leading to interference.
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4.10 ELIMINATION OF INTERFERENCE
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1) Use of a larger pressure angle can eliminate interference. As per the equation 4.8,
having a larger pressure angle results in a smaller base circle. As a
result, more of the tooth profiles become involute. In this case, the
tip of the tooth of one gear will not have a chance to contact the flank
of the other gear on its non-involute portion. Gears are generally
produced with larger pressure angle of 20° with full depth involute
system. The advantages of 20° -pressure angle system are:
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.......................(i) Stronger tooth with higher load carrying capacity
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.......................(ii) Greater length of contact
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However, the 14.5° -pressure angle system is quieter in operation. For a
20° -full depth system, the standard proportions of the gear tooth are:
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a = m
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b = 1.25m
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c = 0.25m
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Tooth thickness = 1.5708m (m is module in mm)
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2) Interference
can be eliminated by under-cutting of tooth. A portion of teeth below
the base circle is cut off. When teeth are produced by this process, the
tip of one tooth of a gear will not contact the noninvolute portion of
the tooth of other gear, hence, elimination of interference. However, if
the undercutting is pronounced, the undercut tooth is considerably
weakened.
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3)
Elimination of interference is possible by tooth stubbing. In this
process a portion of the tip of the teeth is removed, thus preventing
that portion of the tip of tooth in contacting the non-involute portion
of the other meshing tooth. In this case also, the teeth are weakened.
Both the tooth undercutting and tooth stubbing may result in less
contact ratio, thus producing more noise.
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4)
Increasing the number of teeth on the gear can also eliminate the
chances of interference. However, if the gears are to transmit more
power, more teeth can be used only by increasing the pitch diameter,
otherwise the smaller-sized teeth may break in transmitting more loads.
This makes the gear larger for a given module. This is rarely desirable,
as there is space constraint in the machine to house larger gears.
Another problem with larger gears is that for a given rotational speed
of the gear, the pitch line velocity would be more, consequently higher
noise levels. The minimum number of teeth to avoid interference (zmin) is given by the following expression
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5) Increasing slightly the centre distance between the meshing gears would also eliminate interference. |
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6)
Using profile shifted gears (gears with non-standard profile) can also
be an option to eliminate interference. In profile shifted meshing
gears, the addendum on the pinion is shorter compared with standard
gears. |
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4.11 EFFECT OF INTERFERENCE ON PERIODIC FAULTS IN FIBRE ASSEMBLIES
Usually, in drafting gear trains,
the drive originates from the front roller and goes to the back drafting
rollers. Defective gears such as the ones having imperfect tooth
(non-involute profile), broken tooth and accumulated grease tangled with
debris and fibres produce interference. The driven gears will have
periodic variation in their angular speed. This results in interference.
This manifests in periodic fault in fibre assemblies viz., sliver,
roving and yarns, especially if the faulty gear is located in the
drafting gear train. The wave lengths of faults can be measured using a
mass based unevenness tester fitted with spectrogram. From the measured
wave lengths, the faults can be localized, i.e., the source faults can
be found with the knowledge of drafts used in each operation/process and
the gearing plans of machines (preparatory and ring spinning machines)
used to produce yarn. Proper maintenance and housekeeping practices can
only eliminate this kind of fault.
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The
following example illustrates how periodic faults are generated in
roving and yarns with faulty gears in a drafting gear train of roving
machine. The drafting gear train of roving machine is given in Fig.4.11.1. The total-, main-, and break-drafts are: 10, 8 and 1.25 respectively assuming that the bottom roller diameter is 2.54 cm.
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If the gear-Z1 is defective :
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For every one revolution of gear Z1, the faulty tooth of gear Z1 transfer different speed to gear Z2. The numbers of revolution of back roller corresponding to each revolution of the gear Z1
is 0.1. The wave length of fault created by the back roller is the
length of material delivered by the back roller during this time, and is
~0.8 cm (π(0.1)(2.54)). This fault is drafted at the back- and
front-drafting zones, and hence the wave length of fault on roving will
be ~8 cm (0.8 x 1.25 x 8). If the draft of the ring spinning machine is
30, then the wave length of yarn fault is ~2.40 m.
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Fig. 4.11.1 Draft gearing plan on a roving machine
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If the gears-Z2 or Z3 are defective :
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For every one revolution of gear Z2 or Z3, the faulty tooth of gear Z2 or Z3 runs at different speed. The numbers of revolution of back roller corresponding to each revolution of the gear Z2 or Z3
is 0.33. The wave length of fault created by the back roller is ~2.63
cm (π(0.33)(2.54)). This fault is drafted at the back- and
front-drafting zones, and hence the wave length of fault on roving would
be ~26.3 cm (8 x 1.25 x 2.63). The wave length of yarn fault is ~7.9 m.
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If the gears-Z4 or Z5 are defective:
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One
rotation of back roller induces a wave length equal to its
circumference and the wave length of periodic fault on roving will be
~79.8 cm, and the yarn will have a periodic fault with wave length ~24
m. Note that the wave length of periodic fault would be long, if the
defective gear is situated far away from driving gear mounted on the
front roller and vice versa. If one of the compounded gears is defective
among the pair (Z1 and Z2 or Z3 and Z4) will create same wave length. The wave length depends only on the position of faulty gear in the gear train.
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Periodic faults of different wave
lengths on sliver can occur while laying the sliver as coils into the
can, if the gears driving the coiler calender rollers, coiler plate,
calender rollers and sliver container are defective.
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4.12 BACK LASH IN GEARS
Backlash
in gears is purposefully created to avoid jamming of gear teeth. This
is one of the design considerations of gears. The space between teeth
must be made larger than the thickness of tooth, both measured on the
pitch circle. Otherwise, the gears could mesh with jamming. The
difference between tooth-space (Ts) and tooth thickness (Tt), both measured on the pitch circle is known as backlash.
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Linear back Lash = (Ts-Tb)
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(4.10)
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However, any amount of backlash greater than
the minimum amount necessary to ensure satisfactory meshing of gears can
result in dynamic instability and position errors in gear trains. In
many applications such as instruments, differential gear trains and
servo-mechanisms require complete elimination of backlash for proper
functioning.
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4.13 INTERNAL GEARS
In internal gear, the teeth are cut on the inside of rim of gear. The meshing gears have the same centers of rotation. Fig. 4.13.1
shows a pinion meshing with an internal gear or annular gear. The
addendum and base circles of the internal gear lie inside the pitch
circle of that gear. The base circle of internal gear lies near the
addendum circle. Further, it is observed that the positions of addendum
and dedendum circles with respect to the pitch circles are reversed
compared to the external spur gears. Internal gears were used in
epicyclic gear trains for depositing slivers in the form of coils into
the cans. The precision of internal gears is much lower than the regular
spur gears. However, they have the characteristics of high load, high
speed and high speed reduction.
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Click on Image to run the animation
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Animation 4.13.1 Operation of internal spur gears
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Fig 4.13.1 Internal spur gears
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4.14 RACK AND PINION
Rack and pinion is used to convert a rotary motion to translating
motion or vice versa (either the pinion drives the rack or the rack
drives the pinion). Fig. 4.14.1
shows a rack in mesh with a pinion. The rack and pinion is used in
consolidating the lap in scutcher of conventional blow rooms (rack
drives the pinion) and to drive the bobbin carriage of roving machines
(pinion drives the rack). Rack can be imagined as a spur gear having an
infinitely large diameter. Therefore the rack has an infinite number of
teeth and a base circle which is infinite distance from the pitch point.
With infinite diameter of base circle, the involute outline of teeth on
rack becomes straight lines.
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Click on Image to run the animation
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Animation 4.14.1 Operation of rack and pinion
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Fig. 4.14.1 Rack and pinion
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| The tooth profile of pinion is involute. The base pitch of the rack is measured along the pressure line. The base pitch (Pb) is related to the circular pitch (pc) of pinion as |
Pb=pccosø .................................................................................(4.11)
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| 4.15 FORCE ANALYSIS IN SPUR GEAR |
| Power is transmitted, when a tooth of input gear exerts a force (Fn) along the pressure line on the tooth of output gear (Fig. 4.15.1). |
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Fig 4.15.1 Force acting on a spur gear tooth and its components
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The force (Fn) is resolved into two components, tangential, (Ft), and radial component, (Fr) which are related to the pressure angle as
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Torque and power transmission
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| The torque (Mt) in N-mm and power in kW transmitted by gear are: |
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Where n is the rotational speed of gear in rpm; and r is the radius of pitch circle in mm respectively.
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Force analysis in a spur gear train
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The
tangential component of force acting on a driver gear is a reaction
force from the driven gear. It acts opposite to the direction of
rotation of driver. The tangential component of force acting on the
driven gear is the force applied by the driving gear. It acts along the
direction of rotation of the driven gear. In a spur gear train shown in Fig. 4.15.2,
the gear A drives the gear B which in turn drives the gear C. The idler
gear ‘B’ is a driven gear while receiving power from the driver ‘A’ and
it acts as a driver while transmitting the power to the gear ‘C’. The
angle between the input and output gears is 90º.
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Fig. 4.15.2 Spur gear train with an idler or carrier gear
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For this spur gear train, free-body diagram of forces acting on all the gears are shown in Fig. 4.15.3.
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Fig. 4.15.3 Free body diagram of forces in a spun gear train
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If the idler is placed at the bottom, then the reaction force still act
upwards but it will be weaker, since the components of reaction force
would be Ft - Fr. This would give Rb = 0.515 F t; whereas W =1.93 Ft. So, it is preferable to place the idler gear over the input and output gears.
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In
the case of input and output gear revolving in clockwise directions,
both the reaction force and weight of idler would act downward. Again
the preferred location of idler is on the top side, if the idler is to
be mounted on moveable arm and not on a rigidly mounted shaft.
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4.16 FACE WIDTH OF GEAR
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The
dimension of face width of gear is an important aspect in the design of
gears. If the face width is too large, there is a possibility of
concentration of load at one end of the gear tooth. This is due to
number of factors such as misalignment of shafts carrying the meshing
gears and the elastic deformation of shafts.
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When the face width is too small, the gear has poor capacity to absorb
the shock loads and vibrations. Further, teeth wear at a faster rate. In
practice, the optimum range of the face width is in between 8 and 10
modules.
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4.17 LUBRICATION OF GEARS
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Gears
must be properly lubricated for satisfactory performance and durability
of gears. They are lubricated by grease or mineral oils or extreme
pressure lubricants. Grease is used only for the applications involving
very low speed and intermittent operations.
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For
medium speed applications, splash lubrication is preferred; where the
gears are enclosed in a box and dipped in a bath of mineral oil. For
heavy-duty application, extreme pressure lubricants are used. They are
mineral oils having some additives to improve the performance of the
oil.
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5.1 HELICAL GEARS
In helical gears, the two meshing gears may be mounted on parallel or
intersecting shafts. The teeth on helical gear are cut at an angle
(helix angle) to the gear axis as shown in Fig. 5.1.1.
The helix angle usually ranges between 15º and 20º. Helical gears are
classified into: ‘Parallel helical gears’, ‘Crossed helical gears’ and
‘Herringbone or Honeycomb gears’. All the helical gears generate thrust
loads on the shafts because of inclined teeth; hence, these must be
taken care while designing the machines.
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Fig. 5.1.1 Pair of helical gears
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Since the helix (or teeth) can slope either in upward or downward
direction, the term ‘right hand’ and ‘left-hand’ helical gears are used
to distinguish them. When a helical gear is viewed in a plane parallel
to the axis of gear and if the right side of the teeth is nearer to the
observer, then it is a right hand gear. The rule is similar to determine
whether a screw is right or left-handed. In the above figure, a ‘right
hand’ gear at the top is meshing with a ‘left hand’ gear at the bottom.
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5.2 PARALLEL HELICAL GEARS
In
parallel helical gears or straight-helical gears, the meshing gears are
mounted on parallel shafts. The hands of the meshing gears are opposite.
For example, a left hand gear drives a right hand gear, or vice versa.
The helix angle of the meshing gears must be same. The shape of the
tooth is an invoute helicoid. The initial contact of spur gear teeth is a
line extending all the way across the face width of the tooth. The
effect is a sudden application of load on the tooth, which, in turn
leads to impact and more noise when employing the spur gears for
high-speed applications. In helical gears, the initial contact is a
point on the leading edge of the tooth that gradually extends along the
diagonal line across the tooth. Parallel helical gears are used for high
speed and high power transmission compared to spur gears. Their
precision and power transmission efficiencies are good, but lower in
comparison to spur gears.
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This gradual engagement of teeth in helical gears transfer load
smoothly, thus they have the ability to transfer heavy loads at high
speeds compared with spur gears. In addition, helical gears have more
teeth in contact compared with spur gears. Due to these factors, helical
gears run more smoothly and quietly at high speeds and under severe
conditions. Because the nature of contact between helical gears, the
contact ratio is of only minor importance and it is the contact area,
which is proportional to the face width of the gear becomes important.
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The
parallel helical gears are used for the applications involving high
speeds, large power transmission, or where noise control is important. A
helical gear is smaller in size compared to spur gear, for the same
number of teeth, speed reduction ratio, power transmission and speed.
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5.3 GEOMETRY OF HELICAL GEARS
Spur gears have the diametral- and circular- pitches. Helical gear geometry requires additional pitches. Figure 5.3.1 shows a portion of the top view of a helical rack. The angle Ψ is the helix angle. The transverse circular pitch (pt) or circular pitch is measured on a plane normal to the shaft axis (A-A plane). The normal circular pitch pn
is the distance between corresponding points of adjacent teeth,
measured on a plane perpendicular to the helix (B-B plane). The axial
pitch (pa) is the distance between corresponding
points of adjacent teeth, measured on a plane parallel to the shaft
axis. For smooth transfer of load, the face width of helical gear (w) is usually made at least 20% longer than the axial pitch (pa).
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Fig 5.3.1 Top view of helical rack
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Two pressure angles are associated with helical gears; one is measured
in the transverse plane (A-A plane) and the other in the normal plane
(B-B plane). Fig. 5.3 shows the tooth profile in the normal and transverse plane.
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Fig. 5.3.2 Tooth profiles of helical gear in the normal and transverse planes
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5.4 FORCE ANALYSIS IN HELICAL GEARS
| The resultant force Fn acting on the tooth of a helical gear (
Fig 5.4.1 ) can be resolved into three components viz. |
Ft = tangential component (N)
Fr = radial component (N)
Fa= axial component or thrust load (N) |
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Fig. 5.4.1 Forces acting on a tooth of helical gear
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5.5 THRUST LOADS IN PARALLEL HELICAL GEARS
A
disadvantage associated with the helical gears is the inclined or
diagonal contact that results in thrust load (axial load) in addition to
the usual tangential and radial loads. Figure 5.5.1 illustrates the direction of thrust loads on the shafts of meshing parallel helical gears.
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Fig. 5.5.1 Thrust loads on shafts with parallel helical gears
(Vertical
arrows show the directions of rotation of gears, and the horizontal
ones represent the directions of thrust loads acting on shafts)
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The direction in which the thrust loads acts
on the shaft is determined by applying the right or left-hand rule to
the driver. For a left hand driver, if the fingers of left hand are
pointed in the direction of rotation of driver, the thumb points in the
direction of the thrust load acting on the shaft of driver. The
direction of thrust load acting on the shaft of driven gear would be in
the opposite direction to that of the driver. Similarly, for the right
hand driver, right hand must be used. The thrust load pushes the shaft
laterally. This damages the bearings carrying the shaft, if the bearings
are not designed to support the axial load. Thus, bearings are required
that that can support thrust load and the usual radial load (Refer the
module on bearings). In a helical gear train, the resultant thrust load
acting on an idler gear shaft is zero.
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The usual range of helix angle is about 15º to 30° . Since the thrust
load varies directly with the magnitude of tangent of helix angle (refer the equation 4.10),
there must be an upper limit on the helix angle in order to avoid
excessive thrust loads. A lower limit is also essential to ensure smooth
transfer of load.
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5.6 CROSSED HELICAL GEARS
The crossed helical gears are used to transmit power between
non-parallel, non-intersecting shafts. They are also called ‘spiral
gears’. If two helical gears are to operate as crossed helical gears,
they must have the same normal pitch and normal pressure angle. The
meshing crossed helical gears do not require having the same helix
angle, nor do they require opposite hand. In most crossed gear
applications, the meshing gears have the same hand.
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The
crossed helical gears have point contact. Over a period of time, the
contact tends to be line contact; the contact still remains poor. They
have poor precision compared to other gears and require good
lubrication. For this reason crossed helical gears are used for
transmission of light loads at low speeds. They also have limited speed
reduction capacity. The angle between the shafts of meshing crossed
helical gears (S) is related to helix angles of the mating gears ( y1 , y2 ) as expressed below:
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Based on the required angle between the shafts on the machine, the hand
and helix angles of the meshing crossed helical gears are selected. Two
such examples are discussed in the subsequent sections.
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5.7 HERRINGBONE GEARS
Herringbone
gears are also referred as ‘honeycomb’ or ‘double helical’ gears. They
are used to transfer large loads without thrust load on the shafts. In
herringbone gears, half of the face of gear is cut with teeth of one
hand; other half has teeth cut with opposite hand, as shown in Figures 5.71 and 5.7.2.
The gears are cut with a centre space or clearance. It is clear that
the thrust loads originating from each set of teeth cancel each other.
In a continuous tooth herringbone gears teeth are cut up to the centre
of gears.
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| Fig. 5.7.1 Herringbone gears: Left- with centre space; Right-without centre space |
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Fig. 5.7.2 Meshing continuous teeth herringbone gears
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5.8 APPLICATIONS OF PARALLEL HELICAL GEARS
Helical
gears are used for high-speed application with rotational speed above
3600 rpm or with pitch line velocity above 1500 m/min and large power
transmissions. They are used where noise control is important. Parallel
helical gears are invariably used in drawing machines (Fig. 5.8.1)
to drive the drafting rollers and coiler rollers as they rotate at very
high speeds. They are also used on the back bottom drafting rollers of
roving and ring spinning machines.
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Fig. 5.8.1 Parallel helical gears train on drawing machine
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Crossed helical gears on card
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The
gear trains transmit motion from calender rollers to coiler rollers
that deposit the sliver into the can of card. A pair of crossed helical
gears is shown in Fig. 5.9.1. The
two meshing gears on the left side are crossed helical gears of left
hand. The bottom crossed helical gear (driver) is compounded to a spur
gear mounted on the shaft of bottom calender roller. The shaft of driven
crossed helical gear (top) is inclined to the driving shaft (bottom).
Both the crossed helical gears are mounted on non-parallel and
non-intersecting shafts. Since, the can (sliver container) must be
placed near the operator (away from the calender rollers) for easy
handling, this arrangement is required. Farther the placement of can
from the calender rollers, larger the helix angle are required on the
crossed helical gears.
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Fig. 5.9.1 Pair of meshing crossed helical gears on a card
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Crosses helical gears on roving machine
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A
very common use of crossed gears is the one where the angle between the
shafts of meshing gears is 90° . For this application, the meshing
gears must have the same hand. One such example is the drive to bobbins
and spindles on roving machines (Fig.5.9.2).
The bobbin shafts and flyer shafts are vertical, whereas the shafts
driving them are horizontally placed. On both the driving shafts of
bobbin and spindle, crossed helical gears of opposite hands are
alternately mounted so that the gears of one hand drives the front row
of bobbins or spindles; whereas the gears of other hand, drives the back
row of bobbins or spindles. The meshing gears are having the same hand.
All the right hand helical gears mounted on the driving shaft mesh with
the right hand gears mounted on the bobbin shafts for the back row of
bobbins. Similarly, pairs of left hand matting gears drive the front row
of bobbins. Due to this arrangement the thrust loads originating from
left hand and right hand gears of the driving shaft cancel each other (Fig 5.9.3). So the need for thrust bearings on the driving shaft is completely eliminated.
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Fig.
5.9.2 Crossed helical gears of left hand (LH) and right hand (RH)
alternately mounted on the driving shaft to drive the front and back
rows of bobbins
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Fig.
5.9.3 Thrust loads originating from LH and RH crossed helical gears
mounted on bobbin driving shaft (horizontal shaft) cancel each other
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5.10 BEVEL GEARS
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Bevel
gears are used to transmit power between two non-parallel shafts. The
shafts may be intersecting or non-intersecting. Bevel gears can be
described as conical gears as they are cut on conical blanks (tapered).
They are not interchangeable and always designed in pairs. The commonly
used bevel gears are: straight, spiral and hypoid based on the geometry
as given below:
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Table 5.10.1 Geometry of bevel gears
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| Description |
Type of bevel gears
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| Straight |
Spiral |
Hypoid |
| Tooth surface |
Straight |
Curved |
Curved |
| Pitch surface |
Cone |
Cone |
Hyperboloid |
| Shafts |
intersecting |
intersecting |
Non-parallel &
non-intersecting |
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5.11 STRAIGHT BEVEL GEARS
The
straight bevel gears are the simplest types of bevel gears. They are
the important gears to transmit power between intersecting shafts.
Straight bevel gears are shown in Fig.5.11.1.
The teeth are cut straight, have a taper, and if extended inward, would
intersect each other on the axis of shaft. The meshing gears have line
contact. Hence, they are not smooth in operation; generate more
vibrations and noise at high-speed. They produce thrust load on shaft
bearings (Fig.5.11.2). Straight
bevel gears are used for speed ratio 1:1. Their precision is as good as
parallel helical gears, but higher than crossed helical gears, spiral
bevel gears, hypoid bevel gears and worm gears.
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Fig. 5.11.1 Straight bevel gears mounted on shafts normal to each others: Left-on loom; Right-on carding machine.
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Fig. 5.11.2 Thrust load on Bevel gears
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5.12 SPIRAL BEVEL GEARS
These gears are mounted on shaft whose axes are intersecting. The pitch surface is conical as shown in Figures 5.12.1 and 5.12.2.
Spiral bevel gears have curved oblique teeth (spiral), which allow
contact to develop gradually and smoothly. They have more contact length
and area and less power transmission efficiency compared to straight
bevel gears. They are useful for high-speed applications and others
requiring less noise and vibration. They are difficult to design and
costly to manufacture, as they require specialized and sophisticated
machinery for their manufacture. They produce more thrust load on shaft
bearings than straight bevel gears.
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Fig. 5.12.1 Spiral bevel gears
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Fig. 5.12.2 Spiral bevel gears on roving machine to release bobbin rail
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Their advantages compared with straight bevel gears at high speeds are:
(a) smoothness and quietness of operation; (b) strength; and (c)
durability due to the followings:
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Longer contact length and larger contact ratio compared to straight bevel gears of same size.
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Teeth engage
gradually, the contact beginning at one end and gradually working over
other end; whereas in the straight bevel gear the contact takes place
along the entire face of the tooth at the same instant.
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5.13 HYPOID BEVEL GEARS
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Hypoid bevel gears (Fig.5.13.1)
are used to connect shafts whose axes do not intersect. They are very
similar to spiral gears. However, their pitch surfaces are hyperpoloids
rather than cones. As a result, their pitch axes do not intersect. They
permit certain amount of sliding action along the direction of tooth
element, which requires good lubrication. Their power transmission
efficiency is poor compared to other straight and spiral bevel gears. In
general, hypoid gears are most desirable for those applications
requiring large speed reduction ratios, nonintersecting shafts, and also
great smoothness and quietness of operation.
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Fig. 5.13.1 Hypoid bevel gears
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5.14 MITER AND ANGULAR BEVEL GEARS
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In
majority of bevel gear drives, the shafts of the meshing gears are 90º
to each other. If the angles between the shafts are 90°, and the two
gears of a pair are having the same number of teeth, then it is called
as “Miter Gear”. A pair of spiral miter gears is shown in Fig.5.14.1.
In some bevel-gear drives, the angles between the shafts may not be
90°, but either more or less than 90° . These gears are called ‘Angular
bevel gears’. A pair of angular bevel gears is shown in Fig.5.14.2.
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Fig. 5.14.1 Spiral miter gears (Meshing gears having same number of teeth and angular separation 90°)
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Fig. 5.14.2 Angular bevel gears (Angle of separation >90°)
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| 5.15 APPLICATIONS OF BEVEL GEARS |
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| Straight bevel gears are used
primarily for low speed application with pitch line velocities up to
300 m/min. They are widely used in textile machines. Few of applications
are listed below: |
- drive to bobbin rail on roving machine
- drive between the doffer and feed roller on low speed carding machines
- drive from calender roller to coiler rollers, top coiler to bottom coiler plates in card, comber and drawing machine
- drive between calender roll and lap stop mechanism-lever in lap former of conventional blow room
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Spiral bevel gears find application in sewing
machines. In hand releasing mechanisms, spiral bevel gears are used
since the hand movement is jerky. Hypoid gears are almost universally
used for automotive applications. The use of hypoid gears in automobiles
permits lowering of the drive shaft and is thus advantageous in the
design of cars with low bodies. The miter gears are used in high speed
carding machine to drive the web doffing from a motor, and drive to
coiler from an outer shaft. Miter gears find applications to coil
slivers into cans.
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5.16 WORM GEARS
Worm gears are used to transmit power between two nonintersecting
shafts, which are right angles to each other. Crossed helical gears are
also used for applications involving nonparallel, non intersecting
shafts; but they are limited in their load transmission capacity. Worm
gear drives are used for large speed reduction ratio of 100:1 or more in
a single stage. This large amount of speed reduction is not possible
with any other gears in a single stage. They are very compact compared
to other gears. Worm gear drives consists of a worm and a worm gear or
wheel which is a helical gear Fig.5.16.1.
The worm is similar to a screw. The threads of the worm have an
involute helicoid profile. The pair of teeth on meshing worm and worm
gear must have the same hand. The teeth on the worm wheel envelop the
threads on the worm giving either a line or an area of contact between
meshing parts.
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Fig. 5.16.1 Worm and worm gear on loom
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One
of the advantages associated with the use of worm gears is that the
tooth engagement occurs without shock prevalent in other gear types. The
meshing of teeth occurs with a sliding action resulting in very quiet
operation. The sliding friction may produce overheating, which must be
dissipated to the surroundings by lubrication. The power transmission
efficiency of worm gears is lower compared to spur gears, parallel
helical gears, and bevel gears; but higher than that of crossed helical
gears. Worm and worm gears produce thrust load on shaft bearings. The
power transmission capacity is low and limited to 100kW.
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Worm
gears are very compact compared to other gears for the same speed
reduction. Provision can be made for self-locking operation, where the
motion is transmitted only from the worm to the worm wheel. This is
advantageous in lifting devices. The worm wheel in general made from
phosphor-bronze alloy, which is costly. The worm is usually made of
hardened alloy steel. The worm is usually cut on a lath, whereas the
gear is hobbed. All the worm gears must be carefully mounted to ensure
proper operation.
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5.17
TERMINOLOGY OF WORM GEARS
A pair of worm gears is designated by four quantities in the order: number of start on worm (z1), numbers of teeth on worm wheel (z2), diametral quotient of the worm (q) and module in mm (m) as, z1/z2/q/m. A simplified diagram of the worm and worm wheel is shown in Fig.5.17.1. The diametral quotient (q) and module (m) are related as,
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q = d1/m .....................................................................(5.15)
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d2 = mz2 ....................................................................(5.16)
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| Where, d1 and d2 are the pitch circle diameter of the worm and worm wheel respectively. |
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Fig. 5.17.1 Terminology of worm gears
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Worm gears can be classified into:
(a) Single envelope/single start worm gear set; and (b) Double
envelope/double start worm gear set. In the former, a single spiral
starts from one end of worm (left) and finishes at other end (right),
forming the threads. In the later, two spirals with phase difference of
180° start at one end and finishes at other end, forming the threads.
Both the set of threads maintain the phase difference all around. When
the worm gear/wheel having z numbers of teeth is rotated through one revolution, the worm will complete z revolution for single start threads. For double start threads, the number revolutions of the worm will be z/2.
This implies that the speed reduction with single start worm gear set
is twice that of double start worm gear set. When the worm gear is
having 100 teeth, the speed reduction ratios (ratio of output speed and
input speed) are 1/100 and 1/50 respectively for the single start and
double start worm gear sets.
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Single envelop worm gear
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In
a single enveloping set, the width of worm gear is cut into concave
surface, thus partially enclosing the worm in meshing as shown in Fig.5.18.1. They are used in applications requiring a high speed reduction and low load transmission.
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Fig. 5.18.1 Single envelope worm gear set on wrap reel
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Double envelop worm gear
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In double envelope worm gear set, both the width of the helical gear and the length of the worm are cut concavely as shown in Fig.5.18.2.
These results in both the worm and gear partially enclose each other.
The double envelop worm set have more teeth in contact; and area contact
rather than line contact, thus permitting greater load transmission.
The double enveloping gears are difficult to mount compared with single
envelope gears. They are used for higher load transmission compared with
single start gears.
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Fig. 5.18.2 Double envelope worm gear set on ring spinning machine
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5.18 CLASSIFICATION OF WORM GEARS
Worm gears can be classified into:
(a) Single envelope/single start worm gear set; and (b) Double
envelope/double start worm gear set. In the former, a single spiral
starts from one end of worm (left) and finishes at other end (right),
forming the threads. In the later, two spirals with phase difference of
180° start at one end and finishes at other end, forming the threads.
Both the set of threads maintain the phase difference all around. When
the worm gear/wheel having z numbers of teeth is rotated through one revolution, the worm will complete z revolution for single start threads. For double start threads, the number revolutions of the worm will be z/2.
This implies that the speed reduction with single start worm gear set
is twice that of double start worm gear set. When the worm gear is
having 100 teeth, the speed reduction ratios (ratio of output speed and
input speed) are 1/100 and 1/50 respectively for the single start and
double start worm gear sets.
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Single envelop worm gear
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In
a single enveloping set, the width of worm gear is cut into concave
surface, thus partially enclosing the worm in meshing as shown in Fig.5.18.1. They are used in applications requiring a high speed reduction and low load transmission.
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Fig. 5.18.1 Single envelope worm gear set on wrap reel
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Double envelop worm gear
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In double envelope worm gear set, both the width of the helical gear and the length of the worm are cut concavely as shown in Fig.5.18.2.
These results in both the worm and gear partially enclose each other.
The double envelop worm set have more teeth in contact; and area contact
rather than line contact, thus permitting greater load transmission.
The double enveloping gears are difficult to mount compared with single
envelope gears. They are used for higher load transmission compared with
single start gears.
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Fig. 5.18.2 Double envelope worm gear set on ring spinning machine
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Fig. 5.18.2 Double envelope worm gear set on ring spinning machine
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5.19 APPLICATIONS OF WORM GEARS
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Worm gears find applications in almost all textile machines. Few applications are listed below:
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Drive between cylinder and flat
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Drive to builder mechanism in ring spinning machine
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Drive to pedal roller of scutcher from top cone pulley to feed roller
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Drive to bottom calender roller of scutcher from lap stop lever.
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Drive to cams
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6.1 GEAR TRAIN
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In
machines, rotary motion is transmitted from one shaft to other. A set
of gears are employed to transmit motion from main shaft of machine to
various revolving elements. A combination of gears employed to transmit
motion from one shaft to other(s) is called ‘Gear train’. (Fig 6.1.1
)
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Fig. 6.1.1 Spur gear train on the head stock of roving machine
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Gear trains are classified into the following:
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Simple gear trains.
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Compound gear trains.
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Reverted gear trains.
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Epicyclic (or planetary) gear trains
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6.3 SIMPLE GEAR TRAIN
| Simple gear trains are shown in
Fig. 6.3.1. Each shaft is mounted with one gear. |
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Fig. 6.3.1 Simple train of gears
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6.4 COMPOUND GEAR TRAIN
In compound gear trains (Fig.6.4.1),
at least one pair of gears is rigidly mounted on a same shaft, thus
that pair has the same numbers of revolution. They are widely used in
textile machines such as drafting and twisting gearing and head stock
gearing.
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Fig. 6.4.1 Compound train of gears
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| The gear transmission ratio of the compound train shown in figure 5.3 is |
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6.5 REVERTED GEAR TRAIN
In a reverted gear train, the first and the last gears have the same axis of rotation (Fig.6.5.1).
If these two gears are mounted on the same shaft, one of them must be
loosely mounted. They find applications in epicyclic gear trains. They
are also used in clocks and machine tools.
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Fig. 6.5.1 Reverted gear trains
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6.6 EPICYCLIC/ PLANETARY GEAR TRAIN
Epicyclic
gear train is the one in which the axes of some of the gears have
motion. The said gear(s) would be revolving about external axis or axes.
Whereas in other gear trains, the axes of all the gears do not have
motion, only the gears rotate on their axes. Planetary gear trains are
often employed to make more compact gear reducer (large speed reduction
in a small volume) compared to other gear trains. Multiple kinematic
combinations (multiple inputs) are possible with planetary gear trains.
Since few gears are revolving around, the bearings are subjected to high
loads; requiring constant lubrication. Hence, planetary gears are
placed in box with lubricants, sometimes in a sealed box inaccessible to
maintenance crew. Their design and manufacturing is complex and require
a very high degree of balance.
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An epicyclic gear train with one degree of freedom is shown in Fig.6.6.1.
The sun gear A is grounded. In other words, it is held stationary. The
arm/lever is pivoted on the axis of gear A and on its other end it
carries a planetary gear B. The gear B is meshing with the sun gear A.
As the arm rotates, the planetary gear B revolves around the periphery
of the gear A and also rotates on its axis since it is meshing with the
sun gear A. The gear B is the output gear. Since the sun gear is
grounded, the gear B gets its input only from the rotation of arm. This
is called ‘one degree of freedom’.
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Fig. 6.6.1 Epicyclic gear trains: One degree of freedom
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6.7 VELOCITY RATIO OF EPICYCLIC GEAR TRAIN
The velocity ratio of an epicyclic gear train is determined by the following methods: (a) Tabulation method; (b) Formula method; and (c) Instant centre method or tangential velocity method. The tabular and formula methods are discussed below.
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Tabulation method
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This
method determines motion of every element in the gear train. This
procedure is based on a kinematic inversion, where two easily
describable parts of the total motion are analyzed separately, then
added together:
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Motion of all components rigidly fixed to the rotating arm; |
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Motion of all the components relative to the arm. |
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| The superposition of the two components is carried out by the following steps: |
a)
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In the
first step, motion with arm is determined. The gears which are grounded
are disconnected from the ground. All the gears are fixed rigidly to
the rotating arm. The arm is rotated with the rigidly attached gears by a
number of revolutions proportional to the angular velocity of the arm.
If the angular speed of arm is not known, then, rotate the arm by ‘+y’
revolutions (+ve rotation corresponds to counterclockwise direction; and
–ve rotation corresponds to clockwise direction). In doing so, all the
gears will get +y revolutions.
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In the second
step, motion of every gear relative to the arm is determined when the
arm is held stationary. In this step, the gears are unlocked from the
arm, and the sun gear is rotated +x revolution (i.e. counterclockwise),
holding the arm stationary. Then, the number of revolutions and signs of
rotations of other elements/gears are noted.
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| c) |
In the third and
final step, the total number of revolution of each element is found by
algebraically adding its numbers of rotations. This is the sum of
revolution from step 1 and step 2. The basic equations for speeds of all
the elements are obtained in this step. Then these equations are solved
by putting the boundary conditions.
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With reference to the Fig 6.6.1, the tabulation of speeds and signs of rotation of all the elements are given in Table 6.7.1.
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Table 6.7.1 Tabulation method to determine speeds of elements of gear train
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Formula method
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| This method is useful for preliminary design of gear train as it is rapid. Referring to Fig.6.6.1
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