Post on 31-Oct-2014
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-1
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-2
Mechanical Transmissions
Chains Belts Gears
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-3
GEAR
CONTENTS•GEAR•TYPES OF GEARS•NOMENCLATURE•APPLICATIONS OF GEARS•VELOCITY RATIO•GEAR TRAINS•EXAMPLE PROBLEMS AND QUESTIONS
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-4
GEAR…..
• Power transmission is the movement of energy from its place of generation to a location where it is applied to performing useful work
• A gear is a component within a transmission device that transmits rotational force to another gear or device
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-5
TYPES OF GEARS
1. According to the position of axes of the shafts.a. Parallel
1.Spur Gear2.Helical Gear3.Rack and Pinion
b. IntersectingBevel Gear
c. Non-intersecting and Non-parallelworm and worm gears
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-6
SPUR GEAR
• Teeth is parallel to axis of rotation
• Transmit power from one shaft to another parallel shaft
• Used in Electric screwdriver, oscillating sprinkler, windup alarm clock, washing machine and clothes dryer
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-7
External and Internal spur Gear…
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-8
Helical Gear
• The teeth on helical gears are cut at an angle to the face of the gear
• This gradual engagement makes helical gears operate much more smoothly and quietly than spur gears
• One interesting thing about helical gears is that if the angles of the gear teeth are correct, they can be mounted on perpendicular shafts, adjusting the rotation angle by 90 degrees
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-9
Helical Gear…
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-10
Herringbone gears
• To avoid axial thrust, two helical gears of opposite hand can be mounted side by side, to cancel resulting thrust forces
• Herringbone gears are mostly used on heavy machinery.
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-11
Rack and pinion
• Rack and pinion gears are used to convert rotation (From the pinion) into linear motion (of the rack)
• A perfect example of this is the steering system on many cars
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-12
Bevel gears
• Bevel gears are useful when the direction of a shaft's rotation needs to be changed
• They are usually mounted on shafts that are 90 degrees apart, but can be designed to work at other angles as well
• The teeth on bevel gears can be straight, spiral or hypoid
• locomotives, marine applications, automobiles, printing presses, cooling towers, power plants, steel plants, railway track inspection machines, etc.
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-13
Straight and Spiral Bevel Gears
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-14
WORM AND WORM GEAR
• Worm gears are used when large gear reductions are needed. It is common for worm gears to have reductions of 20:1, and even up to 300:1 or greater
• Many worm gears have an interesting property that no other gear set has: the worm can easily turn the gear, but the gear cannot turn the worm
• Worm gears are used widely in material handling and transportation machinery, machine tools, automobiles etc
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-15
WORM AND WORM GEAR
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-16
NOMENCLATURE OF SPUR GEARS
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-17
NOMENCLATURE….
• Pitch surface: The surface of the imaginary rolling cylinder (cone, etc.) that the toothed gear may be considered to replace.
• Pitch circle: A right section of the pitch surface. • Addendum circle: A circle bounding the ends of the teeth, in
a right section of the gear. • Root (or dedendum) circle: The circle bounding the spaces
between the teeth, in a right section of the gear. • Addendum: The radial distance between the pitch circle and
the addendum circle. • Dedendum: The radial distance between the pitch circle and
the root circle. • Clearance: The difference between the dedendum of one gear
and the addendum of the mating gear.
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-18
NOMENCLATURE….
• Face of a tooth: That part of the tooth surface lying outside the pitch surface.
• Flank of a tooth: The part of the tooth surface lying inside the pitch surface.
• Circular thickness (also called the tooth thickness): The thickness of the tooth measured on the pitch circle. It is the length of an arc and not the length of a straight line.
• Tooth space: pitch diameter The distance between adjacent teeth measured on the pitch circle.
• Backlash: The difference between the circle thickness of one gear and the tooth space of the mating gear.
• Circular pitch (Pc) : The width of a tooth and a space, measured on the pitch circle.
N
DPc
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-19
NOMENCLATURE….
• Diametral pitch (Pd): The number of teeth of a gear unit pitch diameter. The diametral pitch is, by definition, the number of teeth divided by the pitch diameter. That is,
Where Pd = diametral pitch N = number of teeth D = pitch diameter
• Module (m): Pitch diameter divided by number of teeth. The pitch diameter is usually specified in inches or millimeters; in the former case the module is the inverse of diametral pitch.
m = D/N
D
NPd
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-20
VELOCITY RATIO OF GEAR DRIVE
d = Diameter of the wheel
N =Speed of the wheel
ω = Angular speed
velocity ratio (n) =
2
1
1
2
1
2
d
d
N
N
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-21
GEAR TRAINS
• A gear train is two or more gear working together by meshing their teeth and turning each other in a system to generate power and speed
• It reduces speed and increases torque
• Electric motors are used with the gear systems to reduce the speed and increase the torque
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-22
Types of Gear Trains
• Simple gear train• Compound gear train• Planetary gear train
Simple Gear Train• The most common of the gear train is the gear pair
connecting parallel shafts. The teeth of this type can be spur, helical or herringbone.
• Only one gear may rotate about a single axis
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-23
Simple Gear Train
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-24
Compound Gear Train
• For large velocities, compound arrangement is preferred
• Two or more gears may rotate about a single axis
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-25
Planetary Gear Train (Epicyclic Gear Train)
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-26
Planetary Gear Train…
• In this train, the blue gear has six times the diameter of the yellow gear
• The size of the red gear is not important because it is just there to reverse the direction of rotation
• In this gear system, the yellow gear (the sun) engages all three red gears (the planets) simultaneously
• All three are attached to a plate (the planet carrier), and they engage the inside of the blue gear (the ring) instead of the outside.
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-27
Planetary Gear Train…
• Because there are three red gears instead of one, this gear train is extremely rugged.
• planetary gear sets is that they can produce different gear ratios depending on which gear you use as the input, which gear you use as the output, and which one you hold still.
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-28
Planetary Gear Train…
• They have higher gear ratios.
• They are popular for automatic transmissions in automobiles.
• They are also used in bicycles for controlling power of pedaling automatically or manually.
• They are also used for power train between internal combustion engine and an electric motor
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-29
Essay type questions
• With sketch explain various types of gears
• With sketch explain three types of gear trains
• With neat sketch explain the nomenclature of spur gear
• Write the applications, advantages and disadvantages of gear drives
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-30
Gears
Gears are machine elements that transmit motion by means of successively engaging teeth.
Gears serve to change the direction of rotation in a mechanical object.
Gear Classification
• Gears may be classified according to the relative position of the axes of revolution. The axes may be
• parallel,
• intersecting,
• neither parallel nor intersecting.
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-31
GEAR…..
• Power transmission is the movement of energy from its place of generation to a location where it is applied to performing useful work
• A gear is a component within a transmission device that transmits rotational force to another gear or device
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-32
TYPES OF GEARS
1. According to the position of axes of the shafts.a. Parallel
1.Spur Gear2.Helical Gear3.Rack and Pinion
b. IntersectingBevel Gear
c. Non-intersecting and Non-parallelworm and worm gears
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-33 33
Gear Trains
Any combination of gear wheels employed to transmit motion from one shaft to the other is called a gear train. The meshing of two gears may be idealized as two smooth discs with their edges touching and no slip between them. This ideal diameter is called the Pitch Circle Diameter (PCD) of the gear.
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-34
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-35
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-36
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-37
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-38
Types of Gears
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-39
Pinion
Gear
Spur Gears
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-40
Spur Gears - Types
External Set: Opposite Movement
Internal Set: Movement in the same direction
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-41
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-42
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-43
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-44
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-45
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-46
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-47
Pinion and Gear
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-48
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-49
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-50
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-51
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-52
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-53
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-54
Nomenclature of Spur Gear Teeth
= (tooth spacing)driven gear – (tooth thickness)driver , measured
on the pitch circle.
Backlash
Pitch circle gear diam.
Fillet radiusClearance
Base Circle
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-55
Gear Tooth Nomenclature
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-56
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-57
The Fundamental Law of Gearing
• The angular velocity ratio between the gears of a gearset remains constant throughout the mesh.
• The angular velocity ratio (mV) is equal to the ratio of the radius of the input gear to that of the output gear
• The torque ratio (mT)
out
in
out
in
in
outV d
d
r
rm
out
in
out
in
in
outV d
d
r
rm
in
out
in
out
out
inT d
d
r
rm
in
out
in
out
out
inT d
d
r
rm
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-58
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-59
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-60
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-61
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-62
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-63
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-64
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-65
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-66
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-67
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-68
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-69
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-70
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-71
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-72
Gear Tooth Nomenclature
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-73
Gear Tooth Nomenclature
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-74
Gear Tooth Nomenclature
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-75
Gear Tooth Nomenclature
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-76
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-77
If mp is 1, then one tooth is leaving contact just as the next is beginning contact. Spur gears [1-2]. The minimum contact ratio for a smooth operation is 1.2. A minimum contact ratio of 1.4 is preferred and larger is better. Most spur gearsets will have contact ratios between 1.4 to 2.
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-78
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-79
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-80
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-81
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-82
The Involute Tooth Form
• The cycloid and the involute: curve characteristics
• The involute is a curve which can be generated by unwrapping a taut string from a cylinder (called the evolute). Features of this involute curve:
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-83
The Involute Tooth Form
• The string is always tangent to the cylinder.• The center of the curvature of the involute is always
at the point of tangency of the string with the cylinder.
• A tangent to the involute is then always normal to the string, the length os which is the instantaneous radius of curvature of the involute curve.
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-84
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-85
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-86
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-87
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-88
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-89
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-90
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-91
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-92
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-93
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-94
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-95
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-96
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-97
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-98
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-99
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-100
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-101
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-102
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-103
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-104
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-105
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-106
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-107
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-108
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-109
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-110
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-111
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-112
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-113
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-114
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-115
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-116
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-117
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-118
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-119
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9-120