ABSTRACTThis project making of the shaft driven chainless bicycle instead of simple chain drive bicycle.7 This idea is consistence performance. Stress analysis on gear and simulation. A shaftdriven bicycle is a chainless bicycle that uses a drive shaft instead of a chain to transmit power from the pedals to the wheel. Shaft drives were introduced over a century ago, but were mostly supplanted by chain-driven bicycles due to the gear ranges possible with sprockets and derailleur. Recently, due to advancements in internal gear technology, a small number of modern shaft-driven bicycles have been introduced. INTRODUCTION A shaft-driven bicycle is a bicycle that uses a drive shaft instead of a chain to transmit power from the pedals to the wheel. Shaft drives were introduced over a century ago, but were mostly supplanted by chain-driven bicycles due to the gear ranges possible with sprockets and derailleur. Recently, due to advancements in internal gear technology, a small number of modern shaft-driven bicycles have been introduced. Shaft-driven bikes have a large bevel gear where a conventional bike would have its chain ring. This meshes with another bevel gear mounted on the drive shaft. The use of bevel gears allows the axis of the drive torque from the pedals to be turned through 90 degrees. The drive shaft then has another bevel gear near the rear wheel hub which meshes with a bevel gear on the hub where the rear sprocket would be on a conventional bike, and cancelling out the first drive torque change of axis. An automotive drive shaft transmits power from the engine to the differential gear of a rear wheel drive vehicle. The drive shaft is usually manufactured in two pieces to increase the fundamental bending natural frequency because the bending natural frequency of a shaft is inversely proportional to the square of beam length and proportional to the square root of specific modulus which increases the total weight of an automotive vehicle and decreases fuel efficiency. So, a single piece drive shaft is preferred here and the material of it is considered to be Titanium alloy because of its high strength and low density. Drive shafts are carriers of torque and are subject to torsion and shear stress, equivalent to the difference between the input torque and the load. They must therefore be strong enough to bear the stress, whilst avoiding too much additional weight as that would in turn increase their inertia. Parker Hannifin is a motion and control technologies corporation; in 2005 they started the Chainless Challenge, it is a competition that was inspired by the cycling community. Since a large portion of Parker’s business focuses on hydraulics they decided to merge the two ideas into a competition. This competition rules are fairly simple develop a 100% human powered bicycle without using any chains to transfer power. This competition was primarily aimed towards students of universities as a senior design project. Each university chosen to compete selects a group of 5-8 seniors to participate. These students start from scratch and design either a hydraulically or pneumatically powered bike to compete in several different races. There was an endurance race, an efficiency race, and a sprint race. The endurance race was an 8 mile course. The efficiency race deals with utilizing an accumulator to store energy for a later use. The sprint race was 100 meter dash to the finish. Each team needs to work together to create a bike that works the best in each race in order to win the Chainless Challenge. This year’s team had four members on it, so the bike development was split into three sections; Chris Clark and Maxton Lown were working the hydraulic power train, Brandon Randal was assigned on the braking system, and Nick Macaluso was assigned to the bike frame. Components 1. Bicycle Chassis 2. Drive shaft 3. Bevel gear 4. History The first shaft drives for cycles appear to have been invented independently in 1890 in the United States and England. A. Fear head, of 354 Caledonian Road, North London developed one in 1890 and received a patent in October 1891.His prototype shaft was enclosed within a tube running along the top of the chain stay; later models were enclosed within the actual chain stay. In the United States, Walter Stillman filed for a patent on a shaft-driven bicycle on Dec. 10, 1890 which was granted on July 21, 1891. The shaft drive was not well accepted in England, so in 1894 Fearn head took it to the USA where Colonel Pope of the Columbia firm bought the exclusive American rights. Belatedly, the English makers took it up, with Humber in particular plunging heavily on the deal. Curiously enough, the greatest of all the Victorian cycle engineers, Professor Archibald Sharp, was against shaft drive; in his classic 1896 book "Bicycles and Tricycles", he writes "The Fearn head Gear.... if bevel-wheels could be accurately and cheaply cut by machinery, it is possible that gears of this description might supplant, to a great extent, the chain-drive gear; but the fact that the teeth of the bevelwheels cannot be accurately milled is a serious obstacle to their practical success". In the USA, they had been made by the League Cycle Company as early as 1893. Soon after, the French company Metropole marketed their Acatane. By 1897 Columbia began aggressively to market the chainless bicycle it had acquired from the League Cycle Company. Chainless bicycles were moderately popular in 1898 and 1899, although sales were still much smaller than regular bicycles, primarily due to the high cost. The bikes were also somewhat less efficient than regular bicycles: there was roughly an 8 percent loss in the gearing, in part due to limited manufacturing technology at the time. The rear wheel was also more difficult to remove to change flats. Many of these deficiencies have been overcome in the past century. In 1902, The Hill-Climber Bicycle Mfg. Company sold a threespeed shaft-driven bicycle in which the shifting was implemented with three sets of bevel gears. [ While a small number of chainless bicycles were available, for the most part, shaft-driven bicycles disappeared from view for most of the 20th century. There is, however, still a niche market for chainless bikes, especially for commuters, and there are a number of manufacturers who offer them either as part of a larger range or as a primary specialization. A notable example is Bio mega in Denmark. Purpose of the Drive Shaft The torque that is produced from the engine and transmission must be transferred to the rear wheels to push the vehicle forward and reverse. The drive shaft must provide a smooth, uninterrupted flow of power to the axles. The drive shaft and differential are used to transfer this torque. Functions of the Drive Shaft a) First, it must transmit torque from the transmission to the differential gear box. b) During the operation, it is necessary to transmit maximum low-gear torque developed by the engine. c) The drive shafts must also be capable of rotating at the very fast speeds required by the vehicle. d) The drive shaft must also operate through constantly changing angles between the transmission, the differential and the axles. As the rear wheels roll over bumps in the road, the differential and axles move up and down. This movement changes the angle between the transmission and the differential. e) The length of the drive shaft must also be capable of changing while transmitting torque. Length changes are caused by axle movement due to torque reaction, road deflections, braking loads and so on. A slip joint is used to compensate for this motion. The slip joint is usually made of an internal and external spline. It is located on the front end of the drive shaft and is connected to the transmission. Now days all automobiles (which are having front engine rear wheel drive) have the transmission shaft as shown in figure. A pair of short drive shafts is commonly used to send power from a central differential, transmission, or transaxle to the wheels. Two piece drive shaft increases the weight of drive shaft which is not desirable in today’s market. Many methods are available at present for the design optimization of structural systems and these methods based on mathematical programming techniques involving gradient search and direct search. The reduction in weight of the drive system is advantageous in overall weight reduction of automobiles which is a highly desirable goal of design engineer. Fig.1.2(a) 3D model of a drive shaft Fig.1.2(b) Position of Drive Shaft LITERATURE REVIEW Introduction Drive shafts are carriers of torque; they are subject to torsion and shear stress, which represents the difference between the input force and the load. They thus need to be strong enough to bear the stress, without imposing too great an additional inertia by virtue of the weight of the shaft. Most automobiles today use rigid driveshaft to deliver power from a transmission to the wheels. A pair of short driveshaft is commonly used to send power from a central differential, transmission, or transaxie to the wheels. There are different types of drive shafts in Automotive Industry: a) 1 piece driveshaft b) 2 piece driveshaft c) Slip in Tube driveshaft The Slip in Tube Driveshaft is the new type which also helps in Crash Energy Management. It can be compressed in case of crash. It is also known as a collapsible drive shaft. Front-wheel drive is the most common form of engine/transmission layout used in modern passenger cars, where the engine drives the front wheels. Most front wheel drive vehicles today feature transverse engine mounting, where as in past decades engines were mostly positioned longitudinally instead. Rear-wheel drive was the traditional standard and is still widely used in luxury cars and most sport cars. Different Types of Shafts 1. Transmission shaft: These shafts transmit power between the source and the machines absorbing power. The counter shafts, line shafts, overhead shafts and all factory shafts are transmission shafts. Since these shafts carry machine parts such as pulleys, gears etc., therefore they are subjected to bending moments in addition to twisting. 2. Machine Shaft: These shafts form an integral part of the machine itself. For example, the crankshaft is an integral part of I.C.engines slider-crank mechanism. 3. Axle: A shaft is called “an axle”, if it is a stationary machine element and is used for the transmission of bending moment only. It simply acts as a support for rotating bodies. Application: To support hoisting drum, a car wheel or a rope sheave. 4. Spindle: A shaft is called “a spindle”, if it is a short shaft that imparts motion either to a cutting tool or to a work- piece. Applications: 1. Drill press spindles-impart motion to cutting tool (i.e.) drill. 2. Lathe spindles-impart motion to work-piece. Apart from, an axle and a spindle, shafts are used at so many places and almost everywhere wherever power transmission is required. Few of them are: 1. Automobile Drive Shaft: Transmits power from main gearbox to differential gear box. 2. Ship Propeller Shaft: Transmits power from gearbox to propeller attached on it. 3. Helicopter Tail Rotor Shaft: Transmits power to rail rotor fan. Part of Drive Shaft Fig 1.3 Demerits of a Conventional Drive Shaft 1. They have less specific modulus and strength. 2. Increased weight. 3. Conventional steel drive shafts are usually manufactured in two pieces to increase the fundamental bending natural frequency because the bending natural frequency of a shaft is inversely proportional to the square of beam length and proportional to the square root of specific modulus. Therefore the steel drive shaft is made in two sections connected by a support structure, bearings and U-joints and hence over all weight of assembly will be more. 4. Its corrosion resistance is less as compared with composite materials. 5. Steel drive shafts have less damping capacity. Merits of Composite Drive Shaft 1. They have high specific modulus and strength. 2. Reduced weight. 3. The fundamental natural frequency of the carbon fiber composite drive shaft can be twice as high as that of steel or aluminum because the carbon fiber composite material has more than 4 times the specific stiffness of steel or aluminum, which makes it possible to manufacture the drive shaft of passenger cars in one piece. A one-piece composite shaft can be manufactured so as to satisfy the vibration requirements. This eliminates all the assembly, connecting the two piece steel shafts and thus minimizes the overall weight, vibrations and the total cost 4. Due to the weight reduction, fuel consumption will be reduced. 5. They have high damping capacity hence they produce less vibration and noise. 6. They have good corrosion resistance. 7. Greater torque capacity than steel or aluminum shaft. 8. Longer fatigue life than steel or aluminum shaft. 9. Lower rotating weight transmits more of available power. Drive Shaft Vibration Vibration is the most common drive shaft problem. Small cars and short vans and trucks (LMV) are able to use a single drive shaft with a slip joint at the front end without experiencing any undue vibration. However, with vehicles of longer wheel base, the longer drive shaft required would tend to sag and under certain operating conditions would tend to whirl and then setup resonant vibrations in the body of the vehicle, which will cause the body to vibrate as the shaft whirls. Vibration can be either transverse or torsional. Transverse vibration is the result of unbalanced condition acting on the shaft. This condition is usually by dirt or foreign material on the shaft, and it can cause a rather noticeable vibration in the vehicle. Torsional vibration occurs from the power impulses of the engine or from improper universal join angles. It causes a noticeable sound disturbance and can cause a mechanical shaking. In excess, both types of vibration can cause damage to the universal joints and bearings. Whirling of a rotating shaft happens when the centre of gravity of the shaft mass is eccentric and so is acted upon by a centrifugal force which tends to bend or bow the shaft so that it orbits about the shaft longitudinal axis like a rotating skipping rope. As the speed rises, the eccentric deflection of the shaft increases, with the result that the centrifugal force also will increase. The effect is therefore cumulative and will continue until the whirling become critical, at which point the shaft will vibrate violently. From the theory of whirling, it has been found that the critical whirling speed of the shaft is inversely proportional to the square of the shaft length. If, therefore, a shaft having, for example, a critical whirling speed of 6000 rev/min is doubled in length, the critical whirling of the new shaft will be reduced to a quarter of this, i.e. the shaft will now begin to rotate at 1500 rev/min. The vibration problem could solve by increasing the diameter of the shaft, but this would increase its strength beyond its torque carrying requirements and at the same time increase its inertia, which would oppose the vehicle’s acceleration and deceleration. Another alternative solution frequently adopted by car, van, and commercial vehicle manufacturers is the use of two-piece drive shafts supported by intermediate or centre bearings. But this will increase the cost considerably. DRIVE MECHANISM Introduction For the gear-like device used to drive a roller chain, see Sprocket. This article is about mechanical gears. For other uses, see Gear (disambiguation)Two meshing gears transmitting rotational motion. Note that the smaller gear is rotating faster. Although the larger gear is rotating less quickly, its torque is proportionally greater. One subtlety of this particular arrangement is that the linear speed at the pitch diameter is the same on both gears. A gear or cogwheel is a rotating machine part having cut teeth, or cogs, which mesh with another toothed part in order to transmit torque, in most cases with teeth on the one gear being of identical shape, and often also with that shape on the other gear. Two or more gears working in tandem are called a transmission and can produce a mechanical advantage through a gear ratio and thus may be considered a simple machine. Geared devices can change the speed, torque, and direction of a power source. The most common situation is for a gear to mesh with another gear; however, a gear can also mesh with a non-rotating toothed part, called a rack, thereby producing translation instead of rotation. The gears in a transmission are analogous to the wheels in a crossed belt pulley system. An advantage of gears is that the teeth of a gear prevent slippage. When two gears mesh, and one gear is bigger than the other (even though the size of the teeth must match), a mechanical advantage is produced, with the rotational speeds and the torques of the two gears differing in an inverse relationship. In transmissions which offer multiple gear ratios, such as bicycles, motorcycles, and cars, the term gear, as in first gear, refers to a gear ratio rather than an actual physical gear. The term is used to describe similar devices even when the gear ratio is continuous rather than discrete, or when the device does not actually contain any gears, as in a continuously variable transmission. The earliest known reference to gears was circa A.D. 50 by Hero of Alexandria, but they can be traced back to the Greek mechanics of the Alexandrian school in the 3rd century B.C. and were greatly Greek polymath Archimedes (287–212 developed by the B.C.). The Antikythera mechanism is an example of a very early and intricate geared device, designed to calculate astronomical positions. Its time of construction is now estimated between 150 and 100 BC. The definite velocity ratio which results from having teeth gives gears an advantage over other drives (such as traction drives and V-belts) in precision machines such as watches that depend upon an exact velocity ratio. In cases where driver and follower are proximal, gears also have an advantage over other drives in the reduced number of parts required; the downside is that gears are more expensive to manufacture and their lubrication requirements may impose a higher operating cost. Types 1. External gear: An external gear is one with the teeth formed on the outer surface of a cylinder or cone. Conversely, 2. Internal gear: an internal gear is one with the teeth formed on the inner surface of a cylinder or cone. For bevel gears, an internal gear is one with the pitch angle exceeding 90 degrees. Internal gears do not cause output shaft direction reversal. List of gears Spur gear Spur gears or straight-cut gears are the simplest type of gear. They consist of a cylinder or disk with the teeth projecting radials, and although they are not straight-sided in form (they are usually of special form to achieve constant drive ratio, mainly involute), the edge of each tooth is straight and aligned parallel to the axis of rotation. These gears can be meshed together correctly only if they are fitted to parallel shafts. Helical gears Helical or "dry fixed" gears offer a refinement over spur gears. The leading edges of the teeth are not parallel to the axis of rotation, but are set at an angle. Since the gear is curved, this angling causes the tooth shape to be a segment of a helix. Helical gears can be meshed unparallel or crossed orientations. The former refers to when the shafts are parallel to each other; this is the most common orientation. In the latter, the shafts are non-parallel, and in this configuration the gears are sometimes known as "skew gears". The angled teeth engage more gradually than do spur gear teeth, causing them to run more smoothly and quietly. With parallel helical gears, each pair of teeth first make contact at a single point at one side of the gear wheel; a moving curve of contact then grows gradually across the tooth face to a maximum then recedes until the teeth break contact at a single point on the opposite side. In skew gears, teeth suddenly meet at a line contact across their entire width causing stress and noise. Skew gears make a characteristic whine at high speeds. Whereas spur gears are used for low speed applications and those situations where noise control is not a problem, the use of helical gears is indicated when the application involves high speeds, large power transmission, or where noise abatement is important. The speed is considered to be high when the pitch line velocity exceeds 25 m/s. A disadvantage of helical gears is a resultant thrust along the axis of the gear, which needs to be accommodated by appropriate thrust bearings, and a greater degree of sliding friction between the meshing teeth, often addressed with additives in the lubricant. Skew gears For a 'crossed' or 'skew' configuration, the gears must have the same pressure angle and normal pitch; however, the helix angle and handedness can be different. The relationship between the two shafts is actually defined by the helix angle(s) of the two shafts and the handedness, as defined: Where is the helix angle for the gear? The crossed configuration is less mechanically sound because there is only a point contact between the gears, whereas in the parallel configuration there is a line contact. Quite commonly, helical gears are used with the helix angle of one having the negative of the helix angle of the other; such a pair might also be referred to as having a right-handed helix and a left-handed helix of equal angles. The two equal but opposite angles add to zero: the angle between shafts is zero – that is, the shafts are parallel. Where the sum or the difference (as described in the equations above) is not zero the shafts are crossed. For shafts crossed at right angles, the helix angles are of the same hand because they must add to 90 degrees. Double helical gears Double helical gears, or herringbone gears, overcome the problem of axial thrust presented by "single" helical gears, by having two sets of teeth that are set in a V shape. A double helical gear can be thought of as two mirrored helical gears joined together. This arrangement cancels out the net axial thrust, since each half of the gear thrusts in the opposite direction resulting in a net axial force of zero. This arrangement can remove the need for thrust bearings. However, double helical gears are more difficult to manufacture due to their more complicated shape. For both possible rotational directions, there exist two possible arrangements for the oppositely-oriented helical gears or gear faces. One arrangement is stable, and the other is unstable. In a stable orientation, the helical gear faces are oriented so that each axial force is directed toward the center of the gear. In an unstable orientation, both axial forces are directed away from the center of the gear. In both arrangements, the total (or net) axial force on each gear is zero when the gears are aligned correctly. If the gears become misaligned in the axial direction, the unstable arrangement will generate a net force that may lead to disassembly of the gear train, while the stable arrangement generates a net corrective force. If the direction of rotation is reversed, the direction of the axial thrusts is also reversed, so a stable configuration becomes unstable, and vice versa. Stable double helical gears can be directly interchanged with spur gears without any need for different bearings. Bevel gear A bevel gear is shaped like a right circular cone with most of its tip cut off. When two bevel gears mesh, their imaginary vertices must occupy the same point. Their shaft axes also intersect at this point, forming an arbitrary non-straight angle between the shafts. The angle between the shafts can be anything except zero or 180 degrees. Bevel gears with equal numbers of teeth and shaft axes at 90 degrees are called miter gears. Spiral bevels Spiral bevel gears can be manufactured as Gleason types (circular arc with non-constant tooth depth), Oerlikon and Curvex types (circular arc with constant tooth depth), KlingelnbergCyclo-Palloid (Epicycloids with constant tooth depth) or KlingelnbergPalloid. Spiral bevel gears have the same advantages and disadvantages relative to their straight-cut cousins as helical gears do to spur gears. Straight bevel gears are generally used only at speeds below 5 m/s (1000 ft/min), or, for small gears, 1000 rpm. Note: The cylindrical gear tooth profile corresponds to an involute, but the bevel gear tooth profile to an octoid. All traditional bevel gear generators (like Gleason, Klingelnberg, Heidenreich&Harbeck, and WMWModule) manufacture bevel gears with an octoidal tooth profile. IMPORTANT: For 5-axis milled bevel gear sets it is important to choose the same calculation / layout like the conventional manufacturing method. Simplified calculated bevel gears on the basis of an equivalent cylindrical gear in normal section with an involute tooth form show a deviant tooth form with reduced tooth strength by 10-28% without offset and 45% with offset [Diss. Hünecke, TU Dresden]. Furthermore those "involute bevel gear sets" causes more noise. Hypoid gear Hypoid gears resemble spiral bevel gears except the shaft axes do not intersect. The pitch surfaces appear conical but, to compensate for the offset shaft, are in fact hyperboloids of revolution. Hypoid gears are almost always designed to operate with shafts at 90 degrees. Depending on which side the shaft is offset to, relative to the angling of the teeth, contact between hypoid gear teeth may be even smoother and more gradual than with spiral bevel gear teeth, but also have a sliding action along the meshing teeth as it rotates and therefore usually require some of the most viscous types of gear oil to avoid it being extruded from the mating tooth faces, the oil is normally designated HP (for hypoid) followed by a number denoting the viscosity. Also, the pinion can be designed with fewer teeth than a spiral bevel pinion, with the result that gear ratios of 60:1 and higher are feasible using a single set of hypoid gears. This style of gear is most commonly found driving mechanical differentials; which are normally straight cut bevel gears; in motor vehicle axles. Backlash Backlash is the error in motion that occurs when gears change direction. It exists because there is always some gap between the trailing face of the driving tooth and the leading face of the tooth behind it on the driven gear, and that gap must be closed before force can be transferred in the new direction. The term "backlash" can also be used to refer to the size of the gap, not just the phenomenon it causes; thus, one could speak of a pair of gears as having, for example, "0.1 mm of backlash." A pair of gears could be designed to have zero backlash, but this would presuppose perfection in manufacturing, uniform thermal expansion characteristics throughout the system, and no lubricant. Therefore, gear pairs are designed to have some backlash. It is usually provided by reducing the tooth thickness of each gear by half the desired gap distance. In the case of a large gear and a small pinion, however, the backlash is usually taken entirely off the gear and the pinion is given full sized teeth. Backlash can also be provided by moving the gears further apart. The backlash of a gear train equals the sum of the backlash of each pair of gears, so in long trains backlash can become a problem. For situations in which precision is important, such as instrumentation and control, backlash can be minimized through one of several techniques. For instance, the gear can be split along a plane perpendicular to the axis, one half fixed to the shaft in the usual manner, the other half placed alongside it, free to rotate about the shaft, but with springs between the two halves providing relative torque between them, so that one achieves, in effect, a single gear with expanding teeth. Another method involves tapering the teeth in the axial direction and providing for the gear to be slid in the axial direction to take up slack. Shifting of gears In some machines (automobiles) it is necessary to alter the gear ratio to suit the task, a process known as gear shifting or changing gear. There are several outcomes of gear shifting in motor vehicles. In the case of vehicle noise emissions, there are higher sound levels emitted when the vehicle is engaged in lower gears. The design life of the lower ratio gears is shorter, so cheaper gears may be used (i.e. spur for 1st and reverse) which tends to generate more noise due to smaller overlap ratio and a lower mesh stiffness etc. than the helical gears used for the high ratios. This fact has been utilized in analyzing vehicle generated sound since the late 1960s, and has been incorporated into the simulation of urban roadway noise and corresponding design of urban noise barriers along roadways. Tooth profile A profile is one side of a tooth in a cross section between the outside circle and the root circle. Usually a profile is the curve of intersection of a tooth surface and a plane or surface normal to the pitch surface, such as the transverse, normal, or axial plane. The fillet curve (root fillet) is the concave portion of the tooth profile where it joins the bottom of the tooth space. The velocity ratio is dependent on the profile of the teeth. Friction and wear between two gears is also dependent on the tooth profile. There are a great many tooth profiles that will give a constant velocity ratio, and in many cases, given an arbitrary tooth shape, it is possible to develop a tooth profile for the mating gear that will give a constant velocity ratio. However, two constant velocity tooth profiles have been by far the most commonly used in modern times. They are the cycloid and the involute. The cycloid was more common until the late 1800s; since then the involute has largely superseded it, particularly in drive train applications. The cycloid is in some ways the more interesting and flexible shape; however the involute has two advantages: it is easier to manufacture, and it permits the center to center spacing of the gears to vary over some range without ruining the constancy of the velocity ratio. Cycloidal gears only work properly if the center spacing is exactly right. Gear materials Numerous nonferrous alloys, cast irons, powder-metallurgy and plastics are used in the manufacture of gears. However, steels are most commonly used because of their high strength-toweight ratio and low cost. Plastic is commonly used where cost or weight is a concern. A properly designed plastic gear can replace steel in many cases because it has many desirable properties, including dirt tolerance, low speed meshing, the ability to "skip" quite well and the ability to be made with materials not needing additional lubrication. Manufacturers have employed plastic gears to reduce costs in consumer items including copy machines, optical storage devices, cheap dynamos, consumer audio equipment, servo motors, and printers. The module system As a result, the term module is usually understood to mean the pitch diameter in millimeters divided by the number of teeth. When the module is based upon inch measurements, it is known as the English module to avoid confusion with the metric module. Module is a direct dimension, whereas diametral pitch is an inverse dimension (like "threads per inch"). DESIGN OF CAST IRON DRIVE SHAFT Introduction A shaft-driven bicycle is a bicycle that uses a drive shaft instead of a chain to transmit power from the pedals to the wheel through contact of gears and a shaft rod to smoothly and efficient. Shaft drives were introduced over a century ago, but were mostly supplanted by chain-driven bicycles due to the gear ranges possible with sprockets and derailleurs. Recently, due to advancements in internal gear technology, a small number of modern shaft-driven bicycles have been introduced. Purpose of the Drive Shaft The torque that is produced from the engine and transmission must be transferred to the rear wheels to push the vehicle forward moment. The drive shaft must provide a smooth, uninterrupted flow of power to the axles. The drive shaft and differential are used to transfer this torque. Functions of the Drive Shaft 1. It must transmit torque from the transmission to the pedal 2. During the operation, it is necessary to transmit maximum low-gear torque 3. The drive shafts must also be capable of rotating at the very fast speeds required by the vehicle. 4. The drive shaft must also operate through constantly changing gear velocity ratio . 5. The length of the drive shaft must also be capable of changing while transmitting torque. Length changes are caused by axle movement due to torque reaction, road deflections, braking loads and so on. A slip joint is used to compensate for this motion. 6. The slip joint is usually made of an internal and external spline. It is located on the front end of the drive shaft and is connected to the transmission. 2 Construction and working principle The term Drive shaft is used to refer to a shaft, which is used for the transfer of motion from one point to another. Whereas the shafts, which propel (push the object ahead) are referred to as the propeller shafts. However the drive shaft of the automobile is also referred to as the propeller shaft because apart from transmitting the rotary motion from the front end to the rear end of the vehicle, these shafts also propel the vehicle forward. The shaft is the primary connection between the front and the rear end (engine and differential), which performs both the jobs of transmitting the motion and propelling the front end. Thus the terms Drive Shaft and Propeller Shafts are used interchangeably. In other words, a drive shaft is a longitudinal power transmitting, used in vehicle where the pedal is situated at the human feet. A drive shaft is an assembly of one or more tubular shafts connected by universal, constant velocity or flexible joints. The number of tubular pieces and joints depends on the distance between the two wheels. The job involved is the design for suitable propeller shaft and replacement of chain drive smoothly to transmit power from the engine to the wheel without slip. It needs only a less maintenance. It is cost effective. Propeller shaft strength is more and also propeller shaft diameter is less. it absorbs the shock. Because the propeller shaft center is fitted with the universal joint is a flexible joint. It turns into any angular position. The both end of the shaft are fitted with the bevel pinion, the bevel pinion engaged with the crown and power is transmitted to the rear wheel through the propeller shaft and gear box. . With our shaft drive bikes, there is no more grease on your hands or your clothes; and no more chain and derailleur maintenance. Shaft-driven bikes have a large bevel gear where a conventional bike would have its chain ring. This meshes with another bevel gear mounted on the drive shaft. The use of bevel gears allows the axis of the drive torque from the pedals to be turned through 90 degrees. The drive shaft then has another bevel gear near the rear wheel hub which meshes with a bevel gear on the hub where the rear sprocket would be on a conventional bike, and canceling out the first drive torque change of axis. The 90-degree change of the drive plane that occurs at the bottom bracket and again at the rear hub uses bevel gears for the most efficient performance, though other mechanisms could be used, e.g. Hobson’s joints, worm gears or crossed helical gears. The drive shaft is often mated to a hub gear which is an internal gear system housed inside the rear hub. Fig 4.1.Bevel Gear Mechanism Specification of drive shaft The specifications of the composite drive shaft of an automotive transmission are same as that of the steel drive shaft for optimal design. The fundamental natural bending frequency for passenger cars, small trucks, and vans of the propeller shaft should be higher than 6,500 rpm to avoid whirling vibration and the torque transmission capability of the drive shaft should be larger than 3,500 Nm. The drive shaft outer diameter should not exceed 100 mm due to space limitations. Here outer diameter of the shaft is taken as 90 mm. The drive shaft of transmission system is to be designed optimally for following specified design requirements as shown in Table. Table: Design requirements and specifications S. Name Notation Unit Value No 1. Ultimate Torque Tmax 2. Max. Speed of shaft Nmax 3. Length of Shaft L Nm rpm mm Steel (SM45C) used for automotive drive shaft applications. The material properties of the steel (SM45C) are given in Table. The steel drive shaft should satisfy three design specifications such as torque transmission capability, buckling torque capability and bending natural frequency. Table: Mechanical properties of Cast iron (SM45C) S.N o Mech.Propertie Symbol s Units 1. Youngs Modulus E GPa 2. Shear Modulus G GPa Cast Iron 3. Poisson Ratio v ------ 4. Density ρ Kg/m3 5. Yield Strength Sy MPa 6. Shear Strength Ss MPa Bevel Gear Bevel gears are gears where the axes of the two shafts intersect and the tooth-bearing faces of the gears themselves are conically shaped. Bevel gears are most often mounted on shafts that are 90 degrees apart, but can be designed to work at other angles as well. The pitch surface of bevel gears is a cone. EOMETRY AND TERMINOLOGY When shafts intersecting are gears, the pitch connected cones by (analogous to the pitch cylinders of spur and helical gears) are tangent along an element, with their apexes at the intersection of the shafts as in Fig. where two bevel gears are in mesh. The size and shape of the teeth are defined at the large end, where they intersect the back cones. Pitch cone and back cone elements are perpendicular to each other. The tooth profiles resemble those of spur gears having pitch radii rbg and rbp and are shown in Fig. 13.3. which explains the nomenclatures of a bevel gear. where Zv is called the virtual number of teeth, p is the circular pitch of both the imaginary spur gears and the bevel gears. Z1 and Z2 are the number of teeth on the pinion and gear, γ1 and γ2 are the pitch cone angles of pinion and gears. It is a practice to characterize the size and shape of bevel gear teeth as those of an imaginary spur gear appearing on the developed back cone corresponding to Tredgold’s approximation. a) Bevel gear teeth are inherently non - interchangeable. b) The working depth of the teeth is usually 2m, the same as for standard spur and helical gears, but the bevel pinion is designed with the larger addendum ( 0.7 working depth). c) This avoids interference and results in stronger pinion teeth. It also increases the contact ratio. d) The gear addendum varies from 1m for a gear ratio of 1, to 0.54 m for ratios of 6.8 and greater. The gear ratio can be determined from the number of teeth, the pitch diameters or the pitch cone angles as, Illustration of spiral angle The Fig.13.4 illustrates the measurement of the spiral angle of a spiral bevel gear. Bevel gears most commonly have a pressure angle of 20o, and spiral bevels usually have a spiral angle of 35 o. Fig. Zero Bevel gears The Fig.13.5 illustrates Zero Bevel gears, which are having curved teeth spiral bevels. But they have zero spiral angels. Comparison of intersecting and offset shaft bevel type gearings Force Analysis Gear and shaft forces Gear and shaft forces Fig. 13.10 Bevel gear - Force analysis In Fig. 13.10, Fn is normal to the pitch cone and the resolution of resultant tooth force Fn into its tangential (torque producing), radial (separating) and axial (thrust) components is designated Ft, Fr and Fa respectively. An auxiliary view is needed to show the true length of the vector representing resultant force Fn (which is normal to the tooth profile). Resultant force Fn is shown applied to tooth at the pitch cone surface and midway along tooth width b. It is also assumed that load is uniformly distributed along the tooth width despite the fact that the tooth width is larger at the outer end Where Vav is in meters per second, dav is in meters, n is in revolutions per minute, Ft is in N and W is power in kW. dav = d-bsin Fn = Ft /cosφ Fr = Fn cosγ = Ft tanφ c Fa = Fn sinγ = Ft tanφ sin Transmission of Torque Action and reaction my friend. If a person does not turn the pedal then he will stand on it and so the maximum torque will = (body mass of the rider x g) x the length of the pedal lever. Remember to consider the gearing of the bike though. The average, fit, adult rider can produce only 75 watts or 1/10hp when cycling at a continuous 12mph (19.3kph)." This usually happens with a pedaling speed of 60-80 rpm though many rider pedal faster. When I cycle, I usually spin at between 100-120 rpm, but I have been riding for years and have found that the higher speed works better for me. Spiral bevel gear A spiral bevel gear is a bevel gear with helical teeth. The main application of this is in a vehicle differential, where the direction of drive from the drive shaft must be turned 90 degrees to drive the wheels. The helical design produces less vibration and noise than conventional straight-cut or spur-cut gear with straight teeth. A spiral bevel gear set should always be replaced in pairs i.e. both the left hand and right hand gears should be replaced together since the gears are manufactured and lapped in pairs. Handedness A right hand spiral bevel gear is one in which the outer half of a tooth is inclined in the clockwise direction from the axial plane through the midpoint of the tooth as viewed by an observer looking at the face of the gear. A left hand spiral bevel gear is one in which the outer half of a tooth is inclined in the counter clockwise direction from the axial plane through the midpoint of the tooth as viewed by an observer looking at the face of the gear. Note that a spiral bevel gear and pinion are always of opposite hand, including the case when the gear is internal. Also note that the designations right hand and left hand are applied similarly to other types of bevel gear, hypoid gears, and oblique tooth face gears. Hypoid gears A hypoid is a type of spiral bevel gear whose axis does not intersect with the axis of the meshing gear. The shape of a hypoid gear is a revolved hyperboloid (that is, the pitch surface of the hypoid gear is a hyperbolic surface), whereas the shape of a spiral bevel gear is normally conical. The hypoid gear places the pinion off-axis to the crown wheel (ring gear) which allows the pinion to be larger in diameter and have more contact area. In hypoid gear design, the pinion and gear are practically always of opposite hand, and the spiral angle of the pinion is usually larger than that of the gear. The hypoid pinion is then larger in diameter than an equivalent bevel pinion. A hypoid gear incorporates some sliding and can be considered halfway between a straight-cut gear and a worm gear. Special gear oils are required for hypoid gears because the sliding action requires effective lubrication under extreme pressure between the teeth. Hypoid gearings are used in power transmission products that are more efficient than conventional worm gearing. They are considerably stronger in that any load is conveyed through multiple teeth simultaneously. By contrast, bevel gears are loaded through one tooth at a time. The multiple contacts of hypoid gearing, with proper lubrication, can be nearly silent, as well. Spiral angle The spiral angle in a spiral bevel gear is the angle between the tooth trace and an element of the pitch cone, and corresponds to the helix angle in helical teeth. Unless otherwise specified, the term spiral angle is understood to be the mean spiral angle. Mean spiral angle is the specific designation for the spiral angle at the mean cone distance in a bevel gear. Outer spiral angle is the spiral angle of a bevel gear at the outer cone distance. Inner spiral angle is the spiral angle of a bevel gear at the inner cone distance. Comparison of spiral bevel gears to hypoid gears Hypoid gears are stronger, operate more quietly and can be used for higher reduction ratios, however they also have some sliding action along the teeth, which reduces mechanical efficiency, the energy losses being in the form of heat produced in the gear surfaces and the lubricating fluid. In older automotive designs, hypoid gears were typically used in rear-drive automobile drive trains, but modern designs have tended to substitute spiral bevel gears to increase driving efficiency. Hypoid gears are still common in larger trucks because they can transmit higher torque. A higher hypoid offset allows the gear to transmit higher torque. However increasing the hypoid offset results in reduction of mechanical efficiency and a consequent reduction in fuel economy. For practical purposes, it is often impossible to replace low efficiency hypoid gears with more efficient spiral bevel gears in automotive use because the spiral bevel gear would need a much larger diameter to transmit the same torque. Increasing the size of the drive axle gear would require an increase of the size of the gear housing and a reduction in the ground clearance. Another advantage of hypoid gear is that the ring gear of the differential and the input pinion gear are both hypoid. In most passenger cars this allows the pinion to be offset to the bottom of the crown wheel. This provides for longer tooth contact and allows the shaft that drives the pinion to be lowered, reducing the "hump" intrusion in the passenger compartment floor. However, the greater the displacement of the input shaft axis from the crown wheel axis, the lower the mechanical efficiency. Worm drive A worm drive is a gear arrangement in which a worm (which is a gear in the form of a screw) meshes with a worm gear (which is similar in appearance to a spur gear). The two elements are also called the worm screw and worm wheel. The terminology is often confused by imprecise use of the term worm gear to refer to the worm, the worm gear, or the worm drive as a unit. Like other gear arrangements, a worm drive can reduce rotational speed or transmit higher torque. The image shows a section of a gear box with a worm gear driven by a worm. A worm is an example of a screw, one of the six simple machines. Explanation A gearbox designed using a worm and worm-wheel is considerably smaller than one made from plain spur gears, and has its drive axes at 90° to each other. With a single start worm, for each 360° turn of the worm, the worm-gear advances only one tooth of the gear. Therefore, regardless of the worm's size (sensible engineering limits notwithstanding), the gear ratio is the "size of the worm gear - to - 1". Given a single start worm, a 20 tooth worm gear reduces the speed by the ratio of 20:1. With spur gears, a gear of 12 smallest teeth (the size if designed to good engineering practices) match with a 240 tooth must to achieve the same ratio. Therefore, if the diametrical pitch (DP) of each gear 20:1 gear is the same, then, in terms of the physical size of the 240 tooth gear to that of the 20 tooth gear, the worm arrangement is considerably smaller in volume. Direction of transmission Unlike with ordinary gear trains, the direction of transmission (input shaft vs output shaft) is not reversible when using large reduction ratios, due to the greater friction involved between the worm and worm-wheel, when usually a single start (one spiral) worm is used. This can be an advantage when it is desired to eliminate any possibility of the output driving the input. If a multistart worm (multiple spirals) is used then the ratio reduces accordingly and the braking effect of a worm and worm-gear may need to be discounted, as the gear may be able to drive the worm. Worm gear configurations in which the gear cannot drive the worm are called self-locking. Whether a worm and gear is selflocking depends on the lead angle, the pressure angle, and the coefficient of friction; however, it is roughly correct to say that a worm and gear are self-locking if the tangent of the lead angle is less than the coefficient of friction. Applications In early 20th century automobiles prior to the introduction of power steering, the effect of a flat or blowout on one of the front wheels tended to pull the steering mechanism toward the side with the flat tire. The use of a worm screw reduced this effect. Further worm drive development led to recirculating ball bearings to reduce frictional forces, which transmitted some steering force to the wheel. This aides vehicle control and reduces wear that could cause difficulties in steering precisely. Worm drives are a compact means of substantially decreasing speed and increasing torque. Small electric motors are generally high-speed and low-torque; the addition of a worm drive increases the range of applications that it may be suitable for, especially when the worm drive's compactness is considered. Worm drives are used in presses, rolling mills, conveying engineering, mining industry machines, on rudders, and worm drive saws. In addition, milling heads and rotary tables are positioned using high-precision duplex worm drives with adjustable backlash. Worm gears are used on many lift/elevator and escalator-drive applications due to their compact size and the non-reversibility of the gear. In the era of sailing ships, the introduction of a worm drive to control the rudder was a significant advance. Prior to its introduction, a rope drum drive controlled the rudder. Rough seas could apply substantial force the rudder, often requiring several men to steer the vessel—some drives had two largediameter wheels so up to four crewmen could operate the rudder. Worm drives have been used in a few automotive rear-axle final drives (though not the differential itself). They took advantage of the location of the gear being at either the very top or very bottom of the differential crown wheel. In the 1910s they were common on trucks; to gain the most clearance on muddy roads the worm gear was placed on top. In the 1920s the Stutz firm used them on its cars; to have a lower floor than its competitors, the gear was located on the bottom. An example from around 1960 was the Peugeot 404. The worm gear carries the differential gearing, which protects the vehicle against rollback. This ability has largely fallen from favour due to the higher-than-necessary reduction ratios. A more recent exception to this is the Torsen differential, which uses worms and planetary worm gears in place of the bevel gearing of conventional open differentials. Torsen differentials are most prominently featured in the HMMWV and some commercial Hummer vehicles, and as a center differential in some all wheel drive systems, such as Audi's quattro. Very heavy trucks, such as those used to carry aggregates, often use a worm gear differential for strength. The worm drive is not as efficient as a hypoid gear, and such trucks invariably have a very large differential housing, with a correspondingly large volume of gear oil, to absorb and dissipate the heat created. Worm drives are used as the tuning mechanism for many musical instruments, including guitars, double-basses, mandolins, bouzoukis, and many banjos (although most highend banjos use planetary gears or friction pegs). A worm drive tuning device is called a machine head. Plastic worm drives are often used on small battery-operated electric motors, to provide an output with a lower angular velocity (fewer revolutions per minute) than that of the motor, which operates best at a fairly high speed. This motor-wormgear drive system is often used in toys and other small electrical devices. A worm drive is used on jubilee-type hose clamps or jubilee clamps. The tightening screw's worm thread engages with the slots on the clamp band. Occasionally a worm gear is designed to run in reverse, resulting in the output shaft turning much faster than the input. Examples of this may be seen in some hand-cranked centrifuges or the wind governor in a musical box. /ong the axis. Differential A differential is a particular type of simple planetary gear train that has the property that the angular velocity of its carrier is the average of the angular velocities of its sun and annular gears. This is accomplished by packaging the gear train so it has a fixed carrier train ratio R = -1, which means the gears corresponding to the sun and annular gears are the same size. This can be done by engaging the planet gears of two identical and coaxial epicyclic gear trains to form a spur gear differential. Another approach is to use bevel gears for the sun and annular gears and a bevel gear as the planet, which is known as a bevel gear differential. Epicyclic differential An epicyclic differential can use epicyclic gearing to split and apportion torque asymmetrically between the front and rear axles. An epicyclic differential is at the heart of the Toyota Prius automotive drive train, where it interconnects the engine, motor-generators, and the drive wheels (which have a second differential for splitting torque as usual). It has the advantage of being relatively compact along the length of its axis (that is, the sun gear shaft). Epicyclic gears are also called planetary gears because the axes of the planet gears revolve around the common axis of the sun and ring gears that they mesh with and roll between. In the image, the yellow shaft carries the sun gear which is almost hidden. The blue gears are called planet gears and the pink gear is the ring gear or annulus. Spur-gear differential This is another type of differential that was used in some early automobiles, more recently the Oldsmobile Tornado, as well as other non-automotive applications. It consists of spur gears only. A spur-gear differential has two equal-sized spur gears, one for each half-shaft, with a space between them. Instead of the Bevel gear, also known as a miter gear, assembly (the "spider") at the centre of the differential, there is a rotating carrier on the same axis as the two shafts. Torque from a prime mover or transmission, such as the drive shaft of a car, rotates this carrier. Mounted in this carrier are one or more pairs of identical pinions, generally longer than their diameters, and typically smaller than the spur gears on the individual half-shafts. Each pinion pair rotates freely on pins supported by the carrier. Furthermore, the pinion pairs are displaced axially, such that they mesh only for the part of their length between the two spur gears, and rotate in opposite directions. The remaining length of a given pinion meshes with the nearer spur gear on its axle. Therefore, each pinion couples that spur gear to the other pinion, and in turn, the other spur gear, so that when the drive shaft rotates the carrier, its relationship to the gears for the individual wheel axles is the same as that in a bevel-gear differential. Application to vehicles A vehicle with two drive wheels has the problem that when it turns a corner the drive wheels must rotate at different speeds to maintain traction. The automotive differential is designed to drive a pair of wheels while allowing them to rotate at different speeds. In vehicles without a differential, such as karts, both driving wheels are forced to rotate at the same speed, usually on a common axle driven by a simple chain-drive mechanism. When cornering the inner wheel travels a shorter distance than the outer wheel, so without a differential either the inner wheel rotates too fast or the outer wheel drags, which results in difficult and unpredictable handling, damage to tires and roads, and strain on (or possible failure of) the entire drive train. In rear-wheel drive automobiles the central drive shaft (or prop shaft) engages the differential through a hypoid gear (crownwheel and pinion) the crown-wheel is mounted on the carrier of the planetary chain that forms the differential. This hypoid gear is a bevel gear that changes the direction of the drive rotation. Loss of traction One undesirable side effect of a conventional differential is that it can limit traction under less than ideal conditions. The amount of traction required to propel the vehicle at any given moment depends on the load at that instant—how heavy the vehicle is, how much drag and friction there is, the gradient of the road, the vehicle's momentum, and so on. The torque applied to each driving wheel is a result of the engine, transmission and drive axles applying a twisting force against the resistance of the traction at that roadwheel. In lower gears and thus at lower speeds, and unless the load is exceptionally high, the drivetrain can supply as much torque as necessary, so the limiting factor becomes the traction under each wheel. It is therefore convenient to define traction as the amount of torque that can be generated between the tire and the road surface, before the wheel starts to slip. If the torque applied to one of the drive wheels exceeds the threshold of traction, then that wheel will spin, and thus only provide torque at each other driven wheel limited by the sliding friction at the slipping wheel. The reduced net traction may still be enough to propel the vehicle. A conventional "open" (non-locked or otherwise traction-aided) differential always supplies close to equal (because of limited internal friction) torque to each side. To illustrate how this can limit torque applied to the driving wheels, imagine a simple rear-wheel drive vehicle, with one rear road wheel on asphalt with good grip, and the other on a patch of slippery ice. It takes very little torque to spin the side on slippery ice, and because a differential splits torque equally to each side, the torque that is applied to the side that is on asphalt is limited to this amount. Based on the load, gradient, et cetera, the vehicle requires a certain amount of torque applied to the drive wheels to move forward. Since an open differential limits total torque applied to both drive wheels to the amount used by the lower traction wheel multiplied by a factor of 2, when one wheel is on a slippery surface, the total torque applied to the driving wheels may be lower than the minimum torque required for vehicle propulsion. Many newer vehicles feature traction control, which partially mitigates the poor traction characteristics of an open differential by using the anti-lock braking system to limit or stop the slippage of the low traction wheel, increasing the torque that can be applied to both wheels. While not as effective in propelling a vehicle under poor traction conditions as a traction-aided differential, it is better than a simple mechanical assistance. open differential with no electronic traction