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    Gear Gear Document Transcript

    • GEAR DRIVES SPUR GEARS Gears are toothed wheels used for transmitting motion and power from one shaft to another when they are not too far apart and when a constant velocity ratio is desired. In comparison with belt, chain and friction drives, gear drives are more compact, can operate at high speeds and can be used where precise timing is required.Also gear drives are used when large power is to be transmitted. Advantages and Limitations of Gear Drive Over Chain and Belt Drives Advantages: 1. Since there is no slip, so exact velocity ratio is obtained. 2. It is capable of transmitting larger power than that of the belt and chain drives. 3. It is more efficient (upto 99%) and effective means of power transmission. 4. It requires less space as compared to belt and rope drives. 5. It can transmit motion at very low velocity, which is not possible with the belt drives. Limitations: 1. The manufacture of gears require special tools and equipments. 2. The manufacturing and maintenance costs are comparatively high. 3. The error in cutting teeth may cause vibrations and noise during operation. Definition of Gear A circular body of cylindrical shape or that of the shape of frustum of a cone and of uniform small width, having teeth of uniform formation, provided on its outer circumferential surface, is called a gear or toothed gear or toothed wheel. CLASSIFICATION OF GEARS Gears may be classified in different manners as given below: 1. Classification based on the relative position of their shaft axes: 2. Classification based on the relative motion of the shafts: 3. Classification based on peripheral speed (v): 4. Classification based on the position of teeth on the wheel: 5. Classification based on the type of gearing: i. External gearing
    • ii. Internal gearing iii. Rack and pinion But from our subject point of view, gears are broadly classified into four groups, viz., spur, helical, bevel and worm gears. Spur gears (sometimes called straight spur gears) have teeth parallel to the axis of rotation are used to transmit motion from one shaft to another parallel shaft. Helical gears have teeth inclined to the axis of rotation. The double helical gears connecting two parallel shafts are known as herringbone gears. Bevel gears have teeth formed on conical surfaces. They are mostly used for transmitting motion between intersecting shafts. A straight-tooth bevel gear. Worm gears consist of a worm and a worm wheel. Worm and worm wheel can be visualized as a screw and nut pair. They are used to transmit motion between non-parallel non-intersecting shafts. SPUR GEARS TERMINOLOGY (a) Circular pitch (pc) It is the distance measured along the circumference of the pitch circle from a point on one tooth to the corresponding point on the adjacent tooth. Circular pitch, Where D = Diameter of pitch circle, and Z = Number of teeth on the wheel. (b) Diametral pitch (pd): It is the ratio of number of teeth to the pitch circle diameter. Diametral pitch,
    • (c) Module pitch (m): It is the ratio of the pitch circle diameter to the number of teeth. Module, Velocity ratio: It is the ratio of speed of driving gear to the speed of the driven gear. Where NA and NB = Speeds of driver and driven respectively, and zA and zB = Number of teeth on driver and driven respectively. Advantages of 141/2 Involute System  It provides smooth and noiseless operation.  It has stronger tooth. Advantages of 200 Involute System  It reduces the risk of undercutting.  It has stronger tooth with a higher load carrying capacity.  It has greater length of contact.
    • GEAR MATERIALS In modern industries, a wide variety of gear materials are used. The gear materials are broadly grouped into two groups viz., metallic and non-metallic materials. 1. Metallic materials: (a) Steel: So far, the most widely used material in gear manufacture is steel. Almost all types of steels have been used for this purpose.  To combine the property of toughness and tooth hardness, steel gears are heat treated.  The plain carbon steels used for medium duty applications are 50 c 8, 45 C 8, 50 C 4 and 55 C 8. For heavy duty applications, alloy steels 40 Cr 1, 30 Ni 4 Cr 1 and 40 Ni 3 Cr 65 Mo 55 are used. For planetary gear trains, alloy steel 35Ni 1 Cr 60 recommended. (b) Cast iron: It is used extensively as a gear material because of its low cost, good machinability, and moderate mechanical properties.  Generally, large size gears are made of grey cast iron of Grades FG 200, FG 260 or FG 350.  Disadvantage: It has low tensile strength. (c) Bronze: It is mainly used in worm gear drives because of their ability to withstand heavy sliding loads.  Bronze gears are also used where corrosion and wear are a problem.  Disadvantage: They are costlier.  The bronze alloys are either aluminium bronze, manganese bronze, silicon bronze, or phosphorus bronze. 2. Non-metallic materials: The non-metallic materials like wood, rawhide, compressed paper and synthetic resins like nylon are used for gears.  Advantages: (i) Noiseless operation; (ii) Cheaper in cost; and (iii) Damping of shock and vibration.  Disadvantages: (i) Low load carrying capacity; and (ii) Low heat conductivity. Selection of Gear Material The selection of the gear material depends upon:
    •  Type of service  Method of manufacture  Wear and shock resistance  Space and weight limitations  Safety and other considerations  Peripheral speed  Degree of accuracy required  Cost of the material  High loads, impact loads, and longer life requirements. GEAR MANUFACTURING Gears can be manufactured by various processes that can be classified under the following three topics. 1. Gear milling: 2. Gear generating:  Hobbing  Shaping 3. Gear molding:  Injection molding  Die casting  Sintering  Investment casting GEAR TOOTH FAILURE The two modes of gear tooth failure are: 1. Tooth breakage (due to static and dynamic loads), and 2. Tooth wear (or surface deterioration) (a) Abrasion, (b) Pitting, and (c) Scoring or seizure
    • 1. Tooth breakage: The load on any gear tooth is cyclic and therefore fatigue fracture of tooth may occur at the root. Tooth breakage may also be caused by an unexpected heavy load imposed on the teeth. 2. Tooth wear (or surface deterioration): (a) Abrasion: When some foreign materials such as dirt, rust or metal particles deposited in between the mating teeth, there will be wear of tooth surfaces. This wear is known as abrasion wear. (b) Pitting and spalling: Pitting is the process during which small pits are formed on the active surfaces of gear tooth. It is a surface fatigue failure which occurs when the load on the gear tooth exceeds the surface endurance strength of the material. (c) Scoring or seizure: Scoring can occur under heavy loads and inadequate lubrication. At this condition, the lubrication oil film breaks down and metal-to-metal contact occurs. Hence high temperatures result and the mating spots of the two surfaces weld together. This phenomenon is known as scoring or seizure. Tooth Stresses (Beam Strength of Gear Tooth – Lewis Equation) The first analysis of gear tooth stresses was done by Wilfred Lewis in 1892. The formula given by Lewis (also known as Lewis equation) still serves as the basis for gear-tooth bending stress analysis. In the Lewis analysis, the gear tooth is considered as a cantilever beam. Assumptions made The Lewis equation is based on the following assumptions:  The effect of radial component Fr, which induces compressive stresses, is negligible.  The tangential component Ft is uniformly distributed across the full face width.  The tangential force Ft is applied to the tip of a single tooth. In other words, it is assumed that at any time only one pair of teeth is in contact and takes the total load.  Stress concentration in the tooth fillet is negligible.  Forces which are due to tooth sliding friction are negligible. DYNAMIC TOOTH LOAD (Buckingham’s Equation for Dynamic Load) In addition to the static load due to power transmission, there are dynamic loads between the meshing teeth. The dynamic loads are due to the following reasons:
    •  Inaccuracies of tooth spacing,  Irregularities in tooth profiles,  Elasticity of parts,  Misalignment between bearings,  Deflection of teeth under load, and  Dynamic unbalance of rotating masses. Let Fd = Total dynamic load on the gear tooth, Ft = Transmitted load i.e., steady load due to transmitted torque, and F1 = Incremental load due to dynamic action. Helical Gears Helical gears are simple modification of ordinary spur gears. A helical gear has teeth in the form of helix around the gear. The use of helical gears is most common in automobiles, turbines and high speed applications. It can be seen that the teeth of the two wheels are of opposite hand. The helixes may be right handed on one wheel and left handed on the other. Advantages of Helical Gears There are three main reasons why helical gears are preferred than spur gears. They are: 1. Noise:Helical gears produce less noise than spur gears of equivalent quality because the total contact ratio is increased. 2. Load carrying capacity: Helical gears have a greater load carrying capacity than equivalent size spur gears because the total length of the line of contact is increased. 3. Manufacturing: A limited number of standard cutters are used to cut a wide variety of helical gears simply by varying the helix angle.
    • Disadvantage of Helical Gears Since the teeth are inclined to the axis of rotation, helical gears are subjected to axial thrust loads. This axial thrust load can be eliminated by using Herringbone (i.e., double helical) gears. TYPES OF HELICAL GEARS 1. Parallel helical gears:  They operate on two parallel shafts.  The magnitude of the helix angle is the same for the pinion and the gear.  They have opposite hand of the helix. i.e., a right hand pinion meshes with a left hand gear and vice versa. 2. Crossed-helical (or spiral) gears:  The operate on two non-parallel shafts.  They have the same or opposite hand of the helix. 1. Helix angle (or Spiral angle) (β): It is the angle between the tooth axis and the plane containing the wheel axis. The helix angle varies from 150 to 250 . 2. Lead: It is the distance advanced by each tooth per revolution measured along the axis parallel to the axis. 3. Transverse circular pitch (pt): The distance between corresponding points on adjacent teeth measured in a plane perpendicular to the shaft axis is known as transverse circular pitch. 4. Axial pitch (pa): The distance between corresponding points on adjacent teeth measured in plane parallel to the shaft axis is known as axial pitch. HERRINGBONE (DOUBLE HELICAL) GEARS Herringbone or double helical gear consists of teeth having a right and left handed helix cut on the same blank. One of the disadvantages of the single helical gear is the existence of axial thrust load. They are eliminated by the Herringbone configuration because the thrust force
    • of the right hand is balanced by that of the left hand helix. Helix angles are usually greater for Herringbone gears than for single helical gears because of the absence of the thrust reactions. Crossed-helical or spiral or screw or skew gears A pair of crossed-helical gears, also known as spiral gears. Spiral gears are used to connect and transmit motion between two non-parallel and non-intersecting shafts. As the contact between the mating teeth is always a point, these gears are suitable only for transmitting a small amount of power. In order for two helical gears to operate as crossed-helical gears, they must have the same normal diametral pitch and normal pressure ϕn. But the gears need not to have the same helix angle or be opposite of hand. In most crossed gear applications, the gears have the same hand. Advantages of Spiral Gears  They provide noiseless operation due to smooth engagement.  They can be used at any angles other than 900 .  They permit a wide range of speed ratios without change of centre distance or gear size. Limitations of Spiral Gears  They transmit relatively small amounts of power because of point contact between teeth.  They have lower efficiency than that of toothed gears because of sliding action.
    • Bevel Gears Bevel gears are used to transmit power between two intersecting shafts. Bevel gears are commonly used in automotive differentials. The gears are formed by cutting teeth along the elements of frustum of a cone. That is, the pitch surface in the bevel gears are truncated cone, one of which rolls over the other. When teeth formed on the cones are straight, the gears are known as straight beveland when inclined, they are known as spiral or helical bevel. Bevel Gear terms Bevel gears are mounted on intersecting shafts at any desired angle, although 90o shaft angle is most common. Bevel gears are not interchangeable. Because they are designed and manufactured in pairs. The bevel gear teeth can be cast, milled, or generated. But the generated teeth is more accurate than cast and milled teeth. TYPES OF BEVEL GEARS Classification Based on the Teeth Shape 1. Straight Bevel Gears
    • 2. Spiral Bevel Gears 3. Zero Bevel Gears 4. Hypoid Gears Worm Gears The worm gears are used to transmit power between two non-intersecting, non-parallel shafts. The angle between the non-intersecting shafts is usually, but not necessarily, a right angle. As discussed in the previous chapters, crossed helical and hypoid gears are also used to connect non-intersecting non-parallel shafts. But crossed-helical and hypoid gears are suitable only for low speed ratios (upto 8) and low power ratings. Whereas worm gears can be used for high speed ratios as high as 300:1. Worm Gear The worm gear drive consists of a worm and a worm wheel. If a tooth of a helical gear makes complete revolutions on the pitch cylinder, the resulting gear is known as a worm.The matting gear is called worm gear or worm wheel. The worm in worm and worm gear drive is same as screw in screw and nut pair. Apllications of Worm Gear Drives Worm gear drives are widely used as a speed reducer in materials handling equipment, machine tools and automobiles. ADVANTAGES AND DISADVNTAGES OF WORM GEAR DRIVE
    • Advantages of Worm Gear Drives  The worm gear drives can be used for speed ratios as high as 300:1.  The operation is smooth and silent.  The worm gear drives are compact compared with equivalent spur or helical gears for the same speed reduction.  The worm gear drives are irreversible. It means that the motion cannot be transmitted from worm wheel to the worm. This property of irreversible is advantageous in load hoisting applications like cranes and lifts. Disadvantages of Worm Gear Drives  The efficiency is low compared with other types of gear drives.  They are costly.  Since sliding occurs, the amount of heat generation is quite high.  The power transmitting capacity of worm gear drive is low (upto 100 kW). TYPES OF WORM GEAR DRIVES Two types of worms in use are: 1. Single-enveloping worm drive: 2. Double-enveloping worm drive: SPECIFICATION OF A PAIR OF WORM GEARS A pair of worm gears can be specified and designated by four parameters as (z1 / z2 / q / mx) Where z1 = Number of starts on the worm, Z2 = Number of teeth on the worm wheel, Q = Diametral quotient or diameter factor = d1/mx, D1 = Pitch circle diameter of the worm, and Mx = Axial module. For example, a R5/25/7/5 worm drive means, a right hand worm of starts 5, meshes with a worm wheel of 25 teeth and of diameter quotient 7, and with module 5 mm. 1.Axial pitch or linear pitch (px): It is the distance between two consecutive teeth, measured
    • along the axis of the worm. In other words, it is the distance between a point on a worm thread and a corresponding point on the adjacent thread measured parallel to the axis. 2. Lead (L): It is the distance travelled by a thread when one complete revolution is given to the worm. Mathematically, Lead, L = px z1 = π mx z1 = Axial pitch Number of threads in the worm 3. Lead angle (γ): It is the angle between the tangent to the pitch helix and the plane of rotation. 4.Helix angle (β): It is the angle between the tangent to the thread helix on the pitch cylinder and the axis of the worm. The worm helix angle is the complement of worm lead angle, i.e., β = 900 γ FAILURE OF WORM GEARING The different worm gear tooth failures are: 1. Seizure:  Since significant sliding occurs between the teeth of the worm wheel and thread of the worm, the possibility of seizure is very high in worm gear drive.  The seizure has greater probability to occur in the zone where oil has squeezed out. 2. Pitting and Rupture:  The worm wheel wears off more. Because the worm wheel is softer than worm.  Only the worm wheel is affected by pitting phenomenon.