Theory of Machines -Lecture2

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Lecture 2

Dr. Nouby M. Ghazaly

Mechanical Engineering Dept., Faculty of Engineering,

South Valley University,

Qena-83523, Egypt.

Email: [email protected]

3/15/2014 1

Theory of Machines -II


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Outline of Presentation

Gear Animation Gear Terminology Velocity Ratio pplications of Gears

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Gear Animation



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Pitch circle, theoretical circle upon which all calculation is based

p, Circular pitch, distance from one teeth to the next, along the pitch circle. p=d/T

m, module=d/T pitch circle/number of teeth p= m


Gear Terminology


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Gear Terminology

Pitch circle: is an imaginary circle that corresponds to thecircumference of the friction gear from which the spur gear isderived.

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 andthe addendum circle.

Dedendum: The radial distance between the pitch circle andthe root circle.

Clearance: The difference between the dedendum of one gearand the addendum of the mating gear.



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Gear Terminology

Face of a tooth: That part of the tooth surface lying outside thepitch surface.

Flank of a tooth: The part of the tooth surface lying inside thepitch surface.

Circular thickness(also called the tooth thickness): Thethickness of the tooth measured on the pitch circle. It is the lengthof an arc and not the length of a straight line.

Backlash: The difference between the circle thickness of one gearand the tooth space of the mating gear.

Circular pitch(Pc) : The width of a tooth and a space, measuredon the pitch circle.

T

DP

c



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Gear Terminology

Diametral pitch (Pd): The number of teeth of a gear unit pitch diameter. Thediametral pitch is, by definition, the number of teeth divided by the pitchdiameter. That is,

Where

Pd= diametral pitchT = number of teeth

D = pitch diameter

Module(m): Pitch diameter divided by number of teeth. The pitch diameter isusually specified in inches or millimeters; in the former case the module is theinverse of diametral pitch.

m = D/T

D

T

Pd



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Basic Gear Design

CENTER TO CENTER DISTANCES OF TWO GEARS

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Basic Gear Design

Gear Ratio (M)

When two friction wheels of different diameter are placed together apoint of the driver gear will travel the same distance as a point ofthe driven gear. Therefore, the number of teeth and the speed of

the gears are directly proportional to its pitch diameter.

M1 = D1 = T1 = RPM2

M2 D2 T2 RPM1

Linear Velocity (V)

Linear velocity is the distance that a given point on the friction wheeltravels during a certain time period.

Linear Velocity (V) = x Pitch Diameter of Gear (D) x RPM



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Factors considered in gearselection

Pitch circle diameter

Number of teeth

Face Width

Material used to manufacture the gear

Style of hub, bore, etc



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A Gear Spur GearCatalog



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A Gear Spur GearCatalog



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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



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Types of Gear Train.

Simple Gear Train

Compound Gear Train

Riveted Gear train

Epicycle Gear Train



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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



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Simple Gear Train

Multiple gears can be connected together to form a gear train.

Each shaft carries only one

gear wheel.

Intermediate gears are known as

Idler Gears.



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Compound Gear Train

DriverCompound

Gear

Driven

If two gear wheels are mounted on a common

shaft then its a Compound Gear train.



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GEAR 'A'

GEAR 'B'

GEAR 'C'

GEAR 'D'

Compound Gears

A

C

BD

Output

Input

Compound Gear train

For large velocities ratios,

compound gear train

arrangement is preferred.

The velocity of each tooth on A

and B are the same so:

ATA= BTB

-as they are simple gears.

Likewise for C and D,

C TC = DTD.



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Reverted Gear Train

When the axes of the first

driver and the last driven

are co-axial, then the

gear train is known as

reverted gear train.

In a reverted gear train, the

motion of the first gear and

the last gear is same.



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Epicyclic Gear Train

Epicyclic means one gear

revolving upon and around

another. The design involves

planet and sun gears as oneorbits the other like a planet

around the sun.

A small gear at the center called

the sun, several medium sizedgears called the planets and a

large external gear called the ring

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Generally, the Gear Ratio is calculated

by counting the teeth of the two gears,

and applying the following formula:

Gear ratio = Number of teeth on driven gear

Number of teeth on driver gear

Gear Ratio



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Gear Ratio - Calculation

A 100 tooth gear drives a 25 tooth

gear. Calculate the gear ratio for the

meshing teeth.

Gear ratio = Number of teeth on driven gear

Number of teeth on driver gear

Gear ratio= driven 25 = 1

driver 100 4

This is written as 1:4



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Gear Speed :- Calculation

A motor gear has 28 teeth and

revolves at 100 rev/min. The

driven gear has 10 teeth. What

is its rotational speed?

Speed of driven gear = Number of teeth on driver gear x 100

Number of teeth on driven gear

Speed of driven gear = driver = 28 x 100 = 280 rev/min

driven 10

28 teeth,

driver

10 teeth,

driven



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Report 1

Different methods of Gear Manufacture



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Questions?

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Theory of Machines -Lecture2

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