Gears-Fundametals [Compatibility Mode]

BITSPilaniPilani Campus

VINAYAK KALLURI

BITSPilaniPilani Campus

BITS Pilani, Pilani Campus

Introduction

Mechanical Drive : a mechanism which is intended to transmit

mechanical power over a certain distance, usually in terms of speed

and torque

Mechanical Drives are classified into two groups according to their

principle of operation

Mechanical drives that transmit power by means of engagement ,

e.g., gear drives and chain drives.

Mechanical drives that transmit power by means of friction , e.g.,

belt drives and rope drives.

The selection of proper mechanical drive for a given application

depends upon number of factors like centre distance, velocity ratio,

shifting arrangement, maintenance considerations and cost.


Gear Drives

Toothed wheels, which transmit power and motion

from one shaft to another by means of successive

engagement of teeth.

Most suitable drive, if the centre distance is small

The efficiency of gear drives is very high compared

to other mechanical drives ( up to 99 %)

Changing a velocity ratio over a wide range is

possible, with the help of special provision called

gear box.


Gear Drives

In any pair of gears, the smaller one is called pinion

and the larger one is called gear immaterial of

which is driving the other

When pinion is the driver, it results in step down

drive in which the output speed decreases and the

torque increases

when the gear is the driver, it results in step up

drive in which the output speed increases and the

torque decreases.


Classification

Gears are arranged between two shafts , which are

1. Parallel

2.Intersecting

3.Non parallel & Non intersecting


Used to transmit motion

between two parallel shafts

Teeth parallel to the axis of

rotation

It has the largest

applications and easy to

manufacture

Spur Gear

Spur Gear


Helical Gear

Also used for parallel shafts, like spur gears

Teeth inclined to the axis of rotation.

The inclined tooth develops thrust loads

Quiet in operation

Teeth engage gradually reducing shocks


Herringbone Gears

Two helical gears with opposing helical angles side-by-side

Axial thrust gets cancelled


Bevel Gear

Teeth formed on conical surfaces and straight teeth tapering towards

an apex

Used for transmitting motion between intersecting shafts

Simple and most commonly used gear in bevel gear family


Spiral Bevel GearA bevel gear with a helical angle of spiral teeth.

More complex to manufacture, but offers a higher

strength and lower noise

Zerol Bevel GearA spiral bevel with zero degree of spiral angle

tooth advance

It has the characteristics of both the straight and

spiral bevel gears

Miter Gear

For one to one ratio

Used to change the direction

Bevel Gear


Hypoid Gear

Crossed Helical Gear

Two helical gears of opposite helix angle will

mesh if their axes are crossed

Strength is very less due to point contact

Also called as screw gears

Similar to spiral bevel gears, but have non

intersecting axis

Blanks of hypoid gears are hyperboloids of

revolution. Hence the name.


Worms and worm gears

oUsed for large speed reductions (more than 3) between two

perpendicular and non-intersecting shafts

o Driver called worm resembles a screw.


GEARS

WormCrossed

helical

BevelHelicalSpur

Intersecting ShaftNon Parallel &

Non Intersecting Shaft

Hypoid

Parallel shaft

Double

(Herringbone)Single

Bevel Spiral BevelZerol Bevel Miter

Classification Summary


Classification: A special cases

Rack and pinion

Comprises a pair of gears which convert rotational motion

into linear motion.

circular pinion engages teeth on a linear "gear( the rack)

Rotational motion applied to the pinion will cause the

rack to move to the side, up to the limit of its travel.


Classification: A special cases

INTERNAL GEAR

Used to transmitting motion between two parallel shafts

Annular wheels are having teeth on the inner periphery

The meshing pinion and annular gear are running in thesame direction


For Different GEARS

Gear Geometry Nomenclature

Gear Force Analysis

Gear tooth Bending strength

Gear tooth Surface fatigue

Design of Gear Drive


NOMENCLATURE


IMPORTANT PARAMETERS OF GEARS


Conjugate Action

Cam A and follower B in

contact. When the

contacting surfaces are

involutes profiles, the

ensuing conjugate action

produces a constant angular-

velocity ratio.


Law of Gearing


Law of Gearing

Because of similar triangles

V1cos = V2cos


Law of Gearing

When two gears are in mesh, their pitch circles roll on

one another without slipping.


Constructing an involute profile

A0-starting point

A1B1=A1A0A2B2=A2A0 and so on

Divide the base circle into

a number of equal parts,

and construct radial lines

OA0, OA1, OA2, etc.

Beginning at A1, construct

perpendiculars A1B1, A2B2,

A3B3, etc.


Involute curve


Gear involute action

To transmit motion at a constant angular-velocity ratio, the pitch point

must remain fixed; that is, all the lines of action for every instantaneous

point of contact must pass through the same point P.


Gear layout circles


Pressure line or line of action and pressure angle

the radius of the base circle, rb = r cos


A template for drawing gear teeth.


Tooth action in involute profiles


Line of action


Tooth Systems

Standard and Commonly Used Tooth Systems for Spur Gears


Tooth Systems

Tooth Sizes in General Uses


Contact Ratio

Arc of action


Problem:

A spur gear set has a module of 4 mm and a velocity ratio of 2.8. the

pinion has 20 teeth. Find the number of teeth on the driven gear, the

pitch diameters, and theoretical center-to-center distance. If a

contact length is 20 mm and pressure angle is 250, then find the

contact ratio.

Ans:

P= m = 12.56 mm

mc = Lab/ p cos = 20/ 12.56 x cos 250 = 1.75


Interference in gears, why it occurs?

1) Due to the presence of non-

involute portion on the tooth

below the base circle

2) Interference is present if C &

D, the points of tangency of

line of action to the base

circles, lie inside the initial and

final points of contact (equal to

the points of intersection of the

line of action with the

addendum circles).


The consequence of interference is cutting away of material

resulting in weakening of the gears against fatigue.

When gear teeth are produced by a generation process,

interference is automatically eliminated because the cutting tool

removes the interfering portion of the flank. This effect is called

as undercutting.

But gear generation is not a solution to interference problem

because the gear would anyway have been weakened in strength.

The solution lies in controlling the minimum number of teeth

on the pinion and the pressure angle.

Rober Lipp (Machine Design, Vol. 54, 1982) carried out a

detailed study on the control of the interference in gears.

Interference in gears


Avoiding Interference in Gears (Robert Liipp study)

For a 20 pressure

angle, with k = 1, NP=13

i.e. 13 teeth on pinion

and gear are

interference-free.


Interference can also be avoided (or reduced) by using a larger pressure angle.

This results in a smaller base circle, so that more of the tooth profile becomes involute.

Thus the demand for smaller pinions with fewer teeth will require the pressure angle of 25 degrees

The pressure angle can not be arbitrarily large because a larger pressure results in

higher bearing loads

Lower the torque capacity and

Decreased contact ratio

L1ab

Interference in Gears


Problem: 138

For a spur gear-set with = 20, while avoiding

interference, find:

(a) The smallest pinion tooth count that will run

with itself

(b) The smallest pinion tooth count at a ratio mG =

2.5, and the largest gear tooth count possible with

this pinion

(c) The smallest pinion that will run with a rack


Parallel Helical Gears

Parallel helical gears are used to transmit motion between parallel

shafts. The helix angle is the same on each gear, but one gear must

have a right-hand helix and the other a left-hand helix.

The initial contact of spur-gear teeth is a line extending all the way

across the face of the tooth. The initial contact of helical-gear teeth

is a point that extends into a line as the teeth come into more

engagement.



In spur gears the line of contact is parallel to the axis of rotation; in

helical gears the line is diagonal across the face of the tooth.

It is this gradual engagement of the teeth and the smooth transfer of

load from one tooth to another that gives helical gears the ability to

transmit heavy loads at high speeds.

Helical gears subject the shaft bearings to both radial and thrust

loads. To avoid thrust, a double helical gear (herringbone) is

equivalent to two helical gears of opposite hand, mounted side by

side on the same shaft.

When two or more single helical gears are mounted on the same

shaft, the hand of the gears should be selected so as to produce the

minimum thrust load.


Standard Tooth Proportions for Helical Gears

[1 mn]

[1.25 mn]


A parallel helical gearset consists of a 19-tooth pinion

driving a 57-tooth gear. The pinion has a left-hand helix

angle of 30, a normal pressure angle of 20, and a normal

module of 2.5 mm. Find:

(a) The normal, transverse, and axial circular pitches

(b) The transverse diametral pitch and the transverse

pressure angle

(c) The addendum, dedendum, and pitch diameter of each

gear

Problem


Solution


Interference in helical gears

The smallest pinion that

run with a rack is

Largest gear with a specified pinion is

Gear ratio mG = NG/NP = m, the smallest pinion tooth count is

The smallest tooth number NP of a helical-spur pinion that will

run without interference with a gear with the same number of

teeth is


Problem: 139

For a helical gear-set with = 20 and = 30

while avoiding interference, find:

(a) The smallest pinion tooth count that will run

with itself

(b) The smallest pinion tooth count at a ratio mG =

2.5, and the largest gear tooth count possible with

this pinion

(c) The smallest pinion that will run with a rack

Gears-Fundametals [Compatibility Mode]

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