Saturday, August 19, 2017

MECHANICS OF TEXTILE MACHINERY - I



1.0 : MACHINE ELEMENTS AND DRIVES
1.1 INTRODUCTION TO DRIVES
In a machine, drives are required to transmit power from electric motor (usually) to various elements and from one element to others so that the various elements could perform their desired operations. Between any two elements of a machine, the one which drives the other is called ‘Driver’; and the other one is termed ‘Driven’. The power/motion is transmitted by means of various drives such as belts, chains and gears. The machine designer has the options of selecting the nature/type of drives. Different drives have certain advantages and limitations. The following factors have to be considered in selecting the natures of drives especially, gears, belts and chains:
1)

Space constraint in housing the driver and driven elements. It is related to availability of space in the machine to house the drives. The compactness of the whole machine puts a limit on the availability of space in the machine.
2)

Accuracy of speeds to be transmitted. In certain operations, the speed transmitted to an element must be very accurate. The speed variation must be kept within a very narrow limit due to process/product requirement.
3) The level of noise the drive system generates and that can be tolerated in the operating environment around the machine.
4) The level of vibrations/shocks the drives produce and their acceptability in terms of efficient functioning of the machines and quality of output from the machines.
5)
Manufacturing accuracies of the drives and the cost associated with them.
The construction of flat-belt, v-belt, round belt, toothed belt, chain drives and various types of gears, analysis of forces, torque and power transmission, characteristics and applications of them are discussed in modules 2 to 5. The comparisons of these drives are also discussed. These modules help the reader on selecting a right type of drive for driving a specific machine element.
The belts must be kept under required tension in order transfer optimum power. Various methods of controlling the belt tensions such as movable-swinging motor and tension pulley are discussed in module 2. The module 3 discusses about chain drives. The classification of chain drives, geometrical relationships, inherent speed variation in chain drives (polygonal effect), characteristics, selection and applications in textile machines are also covered in the module 3.
Spur gears are extensively used in textile machines. The nomenclature used in spur gears and relationships between design parameters of spur gears, requirement of constant speed ratio (conjugate action), generation of involute teeth on spur gear, and effect of interference in gears on periodic drafting waves on fibre strands using roller drafting (drawing, roving and ring spinning machines), and elimination of interference are discussed in module 4. Derivatives of spur gears as internal gears, rack-and-pinion and their applications in textile machines are also discussed in this module. Parallel helical gears, crossed helical gears, different bevel gears and worm gears are used in textile machines. The geometry of these gears, thrust load acting on shaft mounted with these gears and applications are discussed in module 5. Gear trains (train of gears) widely used on machines to transfer motion from one element to many elements. Module 6 deals with many types of gear trains. 

1.2 PRIMARY MACHINE ELEMENTS
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.
  1.3 SPECIAL PURPOSE DRIVES
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.
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. 
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.
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.
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.
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.
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.
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.
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.

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.
Leather belts
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.
Fig. 2.2.1 Three-ply leather flat-belt
Reinforced belt
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.
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.
Pulleys for flat belt
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.

2.3 ANALYSIS OF FLAT BELT TENSIONS
Consider a small element of a flat belt resting over a pulley shown in Fig. 2.3.1.
Fig. 2.3.1 Forces acting on an element of a flat-belt
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)
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.
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.
Click on Image to run the animation
Fig. 2.4.1 Open belt drive with slack side on top of pulleys
Animation: 2.4.1 Moving open belt with slack side on top of pulleys
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.
2.5 MAXIMIZING THE POWER TRANSMISSION


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.
Fig. 2.6.1 Crossed belt on a high speed card
Fig. 2.6.2 Geometry of flat-belt drives: Top-Open belt; Bottom- Crossed belt
The contact angles (in degrees) of open belt over the smaller (driver) and larger (driven) pulleys (Fig. 2.6.2) are given below:

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.
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.

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).
Fig. 2.8.1 Reversing drives with open flat belt
Fig. 2.8.2 Reversing drives with crossed flat belt

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.
Fig. 2.9.1 Flat belt on out-of-plane pulleys driving coiler on carding machine
Fig. 2.9.2 Quarter-twist flat-belt drive (Pulleys are out-of-plane by 90°)
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.
Fig. 2.10.1 Flat belt on fast and loose pulleys
Animation 2.10.1 Flat belt driving fast and loose pulleys
Fig. 2.10.1 (b) Flat belt on fast and loose pulleys mounted on cylinder shaft of a card


2.11 APPLICATIONS OF FLAT BELTS
Some of the applications of flat belts are given below:
Drives to beaters on conventional blow rooms.
Crossed flat-belt transmits drives from cylinder to flat on old cards.
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.
Drive to drafting rollers and other rolling elements on a single delivery drawing machine.
Drives to opening rollers, friction drums and take-off rollers on friction spinning machine.
Drive to rotor on rotor-spinning machine.
Main drive on draw-texturing machine.
Drive to creel-rollers of a high speed drawing machine.

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.
Fig. 2.12.1 (a) V belt drive on a laboratory model card
Fig. 2.12.1 (b) V belt drive on a loom
Fig. 2.12.1 (c) V belt drive on a roving machine
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.
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.
Fig. 2.13.1 Geometry of a V belt
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.
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.
Fig. 2.13.2 Cross-section of a V belt
  2.14 FORCE ANALYSIS IN V BELT
Fig. 2.14.1 Forces on a V belt
2.15 APPLICATIONS OF V BELTS
Few applications of V belts are listed below:
  • Main drives (drive from motor) in all spinning, yarn preparatory, texturing machines, looms, warping and winding machines and compressors.
  • Drive from top coiler to base coiler plate of high speed carding machine.
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).
Fig. 2.16.1 Round belt drive on friction spinning machine
Fig. 2.16.2 Line sketch of round belt drive on friction spinning machine
  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.
Fig. 2.17.1 Timing-belt drive
Characteristics of toothed belt drive
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.
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.
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.
Applications of toothed belts
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.
Fig. 2.17.2 Timing belt drive on air-jet texturing and carding machines
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.
Fig. 2.17.3 Tension wheel on a timing belt drive
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.
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 ).
Fig. 2.18.1 Four-spindle group-drive system with tape
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.
2.19 VARIABLE SPEED DRIVES
Cone and stepped pulleys
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.
Click on Image to run the animation
Animation 2.19.1 Variable speed using cone pulleys
Fig. 2.19.1 Variable speed drive with cone pulleys
Click on Image to run the animation
Animation 2.19.2 Variable speeds with stepped pulleys
Fig. 2.19.2 Variable speed drive with stepped pulleys
Conical discs
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.
Fig. 2.19.3 Speed variation using conical discs on ring spinning machine
Click on Image to run the animation
Animation 2.19.4 Speed variations with conical discs
Fig. 2.19.4 Speed control on ring spinning using conical discs
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.

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.
Movable and swinging motors
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.
Fig. 2.20.1 (a) Motor mounted on movable flat bed on a loom
Fig. 2.20.1 (b) Motor mounted on movable flat bed
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.
Fig. 2.20.2 Swing motor drives on Bale opener
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,
Fig. 2.20.3 Forces acting on a pivoted motor drive
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,
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).
Fig. 2.20.4 Spring loaded idler pulley on friction spinning machine
 
Fig. 2.20.5 Weighted idler pulley
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.
A flat-belt drives lickerin and cylinder through adjustable tension pulley on a high speed carding machine ( Fig. 2.20.6).
Fig. 2.20.6 Flat belt drive to lickerin and cylinder with tension pulley
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.


2.21 COMPARISON OF FLAT AND V BELTS
The advantages of flat belts in compared to V belts are listed below:
  • 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.
  • The periodic adjustment of belt tension and replacement of belts when worn out are easier in the case of tapes and flat belts.
  • Precise alignment of pulleys and shafts are not so critical with tapes and flat belts.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • The creep in tapes, V-belts and round belts are higher compared to timing belt and flat belts.
  • 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.
  • 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="">
  • 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.
  • 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.

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.
Fig. 3.1.1 Chain drive



  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.
Fig. 3.2.1 Construction of a roller chain
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.

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.
Fig. 3.3.1 Single roller or simple chain on bale opener
Fig. 3.3.2 Simple and duplex roller chains on opening and cleaning machine
  3.4 LUBRICATION OF ROLLER CHAINS
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. 


  3.5 CHAIN TENSION AND BENDING FORCE ON SHAFT
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.
Fig. 3.5.1 Forces acting on chain sprockets



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.
Fig. 3.6.1 Geometry of a chain drive


3.9 APPLICATIONS OF ROLLER CHAINS
Few applications of roller chains are listed below:
Pedal roller of scutcher.
Drives from beater to plain and perforated drums and feed rollers on fine cleaner are through duplex roller chains.
Drive from inclined lattice to feed apron and creel apron of bale opener through clutch.
Motor to feed-roller, lap winding-roller, and tuft-feeder in high production carding machine.
Duplex roller chain transmits motion from main shaft to lap rollers via bottom calender roller on sliver lap machine.
Drive to shafts driving the flyers and bobbins on conventional roving machines.
Drive to ring rail on ring spinning machines.
Drive to creel rollers on drawing machines, and hank meters ( Fig. 3.9.1).
Fig. 3.9.1 Chain drive for hank meter on drawing machine
Drive to brush roller shaft on comber.
Drive to drafting rollers that feed sheath fibres on friction spinning machine.
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.
Fig. 3.9.2 Drive to table rollers on a conventional drawing machine


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).
Fig. 4.1.1 Normal or external spur gears on ring spinning machine
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.

4.2 DESIGN ASPECTS OF SPUR GEAR
Nomenclature of spur gear :
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.
Fig. 4.2.1 Terminology of spur gears
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)
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’.
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).
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.
Geometrical relationships in spur gears :
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
(ω1 / ω2 ) = constant. ................................................................(4.5)
Where ω1 = Angular velocity of the driver.
ω2 = Angular velocity of the driven.
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.
Click on Image to run the animation
Animation 4.3.1 Illustration of conjugate action
Fig. 4.3.1 Principles of conjugate action


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).
Click on Image to run the animation
Animation 4.4.1 Illustration of involute generation on a cylinder
Fig 4.4.1 Generation of involute on a cylinder
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.
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.
 

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.
Fig. 4.5.1 Principles of generation of involute profile for gear teeth
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.
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.
Click on Image to run the animation
Animation 4.6.1 Illustration on construction of involute gear tooth
Fig. 4.6.1 Construction of involute gear tooth
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.
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.

4.7 CONTACT RATIO

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.
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:
Fig. 4.8.1 Pressure angle and radii of base and pitch circles



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:
Fig. 4.8.1 Pressure angle and radii of base and pitch circles
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:
Fig. 4.8.1 Pressure angle and radii of base and pitch circles


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:




















Fig. 4.8.1 Pressure angle and radii of base and pitch circles

4.9 INTERFERENCE IN GEARS
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.
Click on Image to run the animation
Animation 4.9.1 Illustration of interference on gears
Fig. 4.9.1 Gears with interference
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.




4.10 ELIMINATION OF INTERFERENCE

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:
.......................(i) Stronger tooth with higher load carrying capacity
.......................(ii) Greater length of contact
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:
a = m
b = 1.25m
c = 0.25m
Tooth thickness = 1.5708m (m is module in mm)
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.
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.
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
5) Increasing slightly the centre distance between the meshing gears would also eliminate interference.
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.

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.
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.
If the gear-Z1 is defective :
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.
Fig. 4.11.1 Draft gearing plan on a roving machine
If the gears-Z2 or Z3 are defective :
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.
If the gears-Z4 or Z5 are defective:
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.
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.

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.
Linear back Lash = (Ts-Tb)
(4.10)
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.

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.
Click on Image to run the animation
Animation 4.13.1 Operation of internal spur gears
Fig 4.13.1 Internal spur gears


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.
Click on Image to run the animation

Animation 4.14.1 Operation of rack and pinion

Fig. 4.14.1 Rack and pinion
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)
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).
Fig 4.15.1 Force acting on a spur gear tooth and its components
The force (Fn) is resolved into two components, tangential, (Ft), and radial component, (Fr) which are related to the pressure angle as
Torque and power transmission
The torque (Mt) in N-mm and power in kW transmitted by gear are:
Where n is the rotational speed of gear in rpm; and r is the radius of pitch circle in mm respectively.
Force analysis in a spur gear train
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.
Fig. 4.15.2 Spur gear train with an idler or carrier gear
For this spur gear train, free-body diagram of forces acting on all the gears are shown in Fig. 4.15.3.
Fig. 4.15.3 Free body diagram of forces in a spun gear train
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.
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.
4.16 FACE WIDTH OF GEAR
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.
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.

4.17 LUBRICATION OF GEARS
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.
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.
 
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.
Fig. 5.1.1 Pair of helical gears
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.

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.
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.
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.
  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).
Fig 5.3.1 Top view of helical rack
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.
Fig. 5.3.2 Tooth profiles of helical gear in the normal and transverse planes
  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)
Fig. 5.4.1 Forces acting on a tooth of helical gear
  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.
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)
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.
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.
 
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.
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:
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.
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.
Fig. 5.7.1 Herringbone gears: Left- with centre space; Right-without centre space
Fig. 5.7.2 Meshing continuous teeth herringbone gears
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.
Fig. 5.8.1 Parallel helical gears train on drawing machine
Crossed helical gears on card
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.
Fig. 5.9.1 Pair of meshing crossed helical gears on a card
Crosses helical gears on roving machine
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.
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
Fig. 5.9.3 Thrust loads originating from LH and RH crossed helical gears mounted on bobbin driving shaft (horizontal shaft) cancel each other
5.10 BEVEL GEARS
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:
Table 5.10.1 Geometry of bevel gears
Description
Type of bevel gears
Straight Spiral Hypoid
Tooth surface Straight Curved Curved
Pitch surface Cone Cone Hyperboloid
Shafts intersecting intersecting Non-parallel &
non-intersecting
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.
Fig. 5.11.1 Straight bevel gears mounted on shafts normal to each others: Left-on loom; Right-on carding machine.
Fig. 5.11.2 Thrust load on Bevel gears
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.
Fig. 5.12.1 Spiral bevel gears
Fig. 5.12.2 Spiral bevel gears on roving machine to release bobbin rail
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:
Longer contact length and larger contact ratio compared to straight bevel gears of same size.
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.

5.13 HYPOID BEVEL GEARS
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.
Fig. 5.13.1 Hypoid bevel gears
5.14 MITER AND ANGULAR BEVEL GEARS
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.
Fig. 5.14.1 Spiral miter gears (Meshing gears having same number of teeth and angular separation 90°)
Fig. 5.14.2 Angular bevel gears (Angle of separation >90°)
5.15 APPLICATIONS OF BEVEL GEARS
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
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.



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.
Fig. 5.16.1 Worm and worm gear on loom
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.
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.
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,
q = d1/m .....................................................................(5.15)
d2 = mz2 ....................................................................(5.16)
Where, d1 and d2 are the pitch circle diameter of the worm and worm wheel respectively.
Fig. 5.17.1 Terminology 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.
Single envelop worm gear
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.
Fig. 5.18.1 Single envelope worm gear set on wrap reel
Double envelop worm gear
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.
Fig. 5.18.2 Double envelope worm gear set on ring spinning machine




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.
Single envelop worm gear
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. 

Fig. 5.18.1 Single envelope worm gear set on wrap reel
Double envelop worm gear
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.
Fig. 5.18.2 Double envelope worm gear set on ring spinning machine

Fig. 5.18.2 Double envelope worm gear set on ring spinning machine

5.19 APPLICATIONS OF WORM GEARS
Worm gears find applications in almost all textile machines. Few applications are listed below:
Drive between cylinder and flat
Drive to builder mechanism in ring spinning machine
Drive to pedal roller of scutcher from top cone pulley to feed roller
Drive to bottom calender roller of scutcher from lap stop lever.
Drive to cams 


6.1 GEAR TRAIN
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 )

Fig. 6.1.1 Spur gear train on the head stock of roving machine

Gear trains are classified into the following:
Simple gear trains.
Compound gear trains.
Reverted gear trains.
Epicyclic (or planetary) gear trains

6.3 SIMPLE GEAR TRAIN
Simple gear trains are shown in Fig. 6.3.1. Each shaft is mounted with one gear.
Fig. 6.3.1 Simple train of gears




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.
Fig. 6.4.1 Compound train of gears
The gear transmission ratio of the compound train shown in figure 5.3 is

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.
Fig. 6.5.1 Reverted gear trains

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.
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’.
Fig. 6.6.1 Epicyclic gear trains: One degree of freedom



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.
Tabulation method
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:
(1) Motion of all components rigidly fixed to the rotating arm;
(2) Motion of all the components relative to the arm.
The superposition of the two components is carried out by the following steps:
a)

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.
b)
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.
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.
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.
Table 6.7.1 Tabulation method to determine speeds of elements of gear train
Formula method
This method is useful for preliminary design of gear train as it is rapid. Referring to Fig.6.6.1 ,








 














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