J3103/2/1GEAR

General Objective : To understand the concept of gears and gearing

Specific Objectives : At the end of the unit you will be able to:

Ø Know the types and functions of gears in engineering.Ø Know, sketch and label the parts of gears.Ø Understand the method of measuring spur gear.

UNIT 2

OBJECTIVES

GEAR

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J3103/2/2GEAR

2.0 INTRODUCTION

Gears are used to transmit power positively from one shaft to another bymeans of successively engaging teeth (in two gears). They are used in place ofbelt drives and other forms of friction drive when exact speed ratios and powertransmission must be maintained. Gears may also be used to increase ordecrease the speed of the driven shaft, thus decreasing or increasing the torqueof the driven number.

2.1. TYPES OF GEARS

2.1.1. Spur gear

Spur gears, Fig. 2.1, are generally used to transmit power betweentwo parallel shafts. The teeth on these gears are straight and parallel tothe shafts to which they are attached. When two gears of different sizesare in mesh, the larger is called the gear while the smaller is called the

pinion. Spur gears are used where slow to moderate- speed drive arerequired.

INPUT

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.

2.1.2. Internal gears

Internal gears, Fig. 2.2., are used where the shafts are parallel andthe centers must be closer together and that could be achieved with spuror helical gearing. This arrangement, provides a stronger drive since

there is the greater area of contact than with the conventional gear drive.It also provides speed reductions with a minimum space requirement.Internal gears are used on heavy duty tractors where much torque isrequired.

2.1.3. Helical gears

Helical gears, Fig.2.3, may be used to connect parallel shafts or

shafts which are at an angle. Because of the progressive rather thanintermittent action of the teeth, helical gears run more smoothly andquietly than spur gears. Since there is more than one tooth inengagement at any one time, helical gears are stronger than spur gears ofthe same size and pitch. However, special bearing (thrust bearings) areoften required on shafts to overcome the end thrust produced by these

gears as they turn.

Figure 2.1. Spur gears Figure 2.2. Internal gears

Gear

Pinion

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J3103/2/4GEAR

2.1.4. Herringbone gears

Herringbone gears, Fig. 2.4., are resembles of two helicalgears placed side by side, with one half having a left-hand helix and the

other half a right-hand helix. These gears have a smooth continuousaction and eliminate the need for thrust bearings.

2.1.5. Bevel gears

When two shafts are located at an angle with their axial linesintersecting at 90o, power is generally transmitted by means of bevelgears, Fig. 2.5.

Figure 2.3. Helical gears Figure 2.4. Herringbone gears

Figure 2.5. Bevel gears

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J3103/2/5GEAR

2.1.6. Miter gears

When the shafts are at right angles and the gears are of the samesize, they are called miter gears, Fig. 2.6..

2.1.7. Angular bevel gears

However, it is not necessary that the shafts be only at right anglesin order to transmit power. If the axes of the shafts intersect at any angleother 90o, the gears are known as angular bevel gears, Fig. 2.7.

2.1.8. Hypoid gears

Bevel gears have straight teeth very similar to spur gears.Modified bevel gears having helical teeth are known as hypoid gears. Theshafts of these gears, although at right angles, are not in the same planeand, therefore, do not intersect. Hypoid gears are used in automobiledrives, Fig. 2.8.

Figure 2.6. Miter gears Figure 2.7. Angular bevel gears

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J3103/2/6GEAR

2.1.9. Worm and worm gear

When shafts are at right angles and considerable reduction in speedis required, a worm and worm gear may be used, Fig. 2.9. The worm,which meshes with the worm gear, may be single or multiple start thread.

A worm with a double-start thread will revolve the worm gear twice asfast as a worm with a single-start thread and the same pitch.

2.1.10. Rack and pinion

When it is necessary to convert rotary motion to linear motion, arack and pinion may be used, Fig. 2.10. The rack, which is actually astraight or flat gear, may have straight teeth to mesh with a spur gear, orangular teeth to mesh with a helical gear.

Figure 2.8. Hypoid gears Figure 2.9. Worm and worm gears

Figure 2.10. Rack and pinion

Worm

Worm gear

Pinion

Rack

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2.2. GEAR TERMINOLOGY

2.2.1. Addendum

Addendum is the radial distance between the pitch circle and theoutside diameter or the height of the tooth above the pitch.

2.2.1. Dedendum

Dedendum is the radial distance from the pitch circle to the bottomof the tooth space.

2.2.3. Pitch diameter

Pitch diameter is the diameter of the pitch circle which is equal to

the outside diameter minus two addendums.

Fig. 2

circular pitch

clea

ranc

e

addendum

dedendum

face width

addendum circle

face

flank

thooththickness

top land/peak

pitch circle

dedendumcircle

root

pitchdiamete outside

diametebase

diamete

pitchliner

Fig. 2.11 Parts of a spur gear

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J3103/2/8GEAR

2.2.4. Base diameter

The diameter of the circle from which the involute is generated;

which is equals to pitch diameter times the cosine of the pressure angle.

2.2.5. Pitch circle

Pitch circle is the circle through the pitch point having its centre atthe axis of the gear.

2.2.6. Pitch line

The line formed by the intersection of the pitch surface and thetooth surface.

2.2.7. Face width - The width of the pitch surface.

2.2.8. Tooth thickness

The thickness of the tooth measured on the pitch circle.

2.2.9. Top land - The surface of the pitch cylinder.

2.2.10. Base diameter - The diameter of the root circle.

2.2.11. Root - The bottoms of the tooth surface.

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J3103/2/9GEAR

2.3. MEASUREMENT AND TESTING OF GEARS

2.3.1. Gear-tooth vernier caliper

The gear-tooth vernier, Fig.2.12, is an instrument for measuringthe pitch-line thickness of a tooth. It has two scales and must be set forthe width (w) of the tooth, and the depth (h) from the top, at which thewidth occurs.

AO = R

Figure 2.12. The gear-tooth vernier caliper

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J3103/2/10GEAR

NOTE: The following considerations of gear elements, the symbolsbelow will be used for the quantities.

T/t = No. of teethP = Diametral pitch ( inch gear )P = Circular pitchD/d = Diameter of pitch circleR/r = Radius of pitch circleY = pressure angle

M = ModulAdd/A = Addendum

Ded/D = DedendumCircular pitch = P x Modul M

The angle subtended by a half tooth at the centre of the gear ( AOB), Fig. 2.12, is given by,

=41 x

T360 =

T90 ; T = no. of teeth

AB =2w = AO sin

T90 = R sin

T90

D = Modul x No. of Teeth, and

R = R2

MT

i.e. D = 2R =MT and R =2

MT

Hence2w = R sin

T90

=2

MT sinT90

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J3103/2/11GEAR

and w = MT sinT90 (1)

To find h we have that h = CB = OC – OB

But OC = R + Add =2

MT +M

And OB = R cosT90 =

2MT cos

T90

Hence h =2

MT +M -2

MT cosT90

=2

MT +M -2

MT cosT90 ] (2)

= M +2

MT [ 1- cosT90 ]

For diametral-pitch gears, (1) becomes w =PT sin

T90

And (2) becomes h =P1 [ 1 +

2T ( 1 – cos

T90 )

Example:To calculate the gear tooth vernier setting to measure a gear of 33T,

6 modul.

w = MT sinT90 = 6 x 33 sin

3390

= 198 sin 2o 43.5’ = 198 x 0.0476

= 9.42 mm.

h = M [ 1 +2T ( 1 – cos

2T )]

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J3103/2/12GEAR

= 6 [ 1 +2

33 ( 1 – cos3390 ) ]

= 6 [ 1 +2

33 (0.0011) ]

= 6.11 mm

2.4. PLUG METHOD OF CHECKING FOR PITCH DIAMETER AND DIVIDEOF TEETH

The tooth vernier gives us a check on the size of the individual tooth, butdoes not give a measure of either the pitch diameter or the accuracy of thedivision of the teeth.

Fig. 2.13 shows a rack tooth symmetrically in mesh with a gear toothspace, the curved sides of the gear teeth touching the straight rack tooth at thepoints A and B on the lines of action. O is the pitch. If now we consider the rack

Figure 2.13

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J3103/2/13GEAR

tooth as an empty space bounded by its outline, a circle with centre at O andradius OB would fit in the rack tooth and touch it at A and B (since OA and OBare perpendicular to the side of the rack tooth). Since the rack touches the gear

at these points, the above circle (shown dotted) will rest against the gear teeth atpoints A and B and will have its centre on the pitch circle.

In triangle OBD: OB = radius of plug required.

OD =41 circular pitch

=4mp

< B = 90o, < O = y

OB = OD cos y

=4mp cos y

Dia of plug = 2OD

=2mp cos y

This is the diameter of a plug which will rest in the tooth space and haveits centre on the pitch circle. Notice that the plug size remains the same for allgears having the same pitch and pressure angle.

With such plugs placed in diametrically opposite tooth spaces, it is asimple matter to verify the gear pitch diameter. The accuracy of the spacing

over any number of teeth may be found as shown in chordal calculations.

Example:Calculate for a 36Tgear of 5 mm module and 20o pressure angle, (a) plug size (b)distance over two plugs placed in opposite spaces, (c) distance over two plugsspaced 10 teeth apart.

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J3103/2/14GEAR

Solutions:

(a) Dia of plug =2mp cos y

=2

5p cos 20o

= 7.854 x 0.9397= 7.38 mm

Pitch dia of gear = mT= 5 x 36

= 180 mm

(b) Distance across plugs in opposite spaces = 180 + 7.38= 187.38 mm

(c) Distance across plugs spaced 10 teeth apart (Fig.2.14)

Angle subtended by 10 teeth = 10 x36360

= 100o.

Figure 2.14

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J3103/2/15GEAR

In triangle OAB:AB = OA sin 50o

= 90 x 0.766

= 68.94Centre distance of plugs = 2 x AB

= 2 x 68.94= 137.88 mm.

Distance over plugs = 137.88 + 7.38= 145.26 mm.

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J3103/2/16GEAR

2.1. State three (3) characteristics of the following gearsi. helical gearii. spur gear

2.2. Sketch and name six (6) parts of a spur gear

ACTIVITY 2

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J3103/2/17GEAR

2.1. (a) 3 characteristics of helical gears;

i) connect parallel shafts or shafts which are at an angleii) runs more smoothly and quietly than spur gears.iii) gears are stronger than spur gears of the same size and pitch.

(b) 3 characteristics of spur gears;

i) transmits power between two parallel shafts.ii) the teeth on these gears are straight and parallel to the shafts to

which they are attached.iii) they are used where slow to moderate-speed drive are required.

2.2.

FEEDBACK ON ACTIVITY 2

circular pitch

clea

ranc

e

addendum

dedendum

face width

addendum circle

face

flank

thooththickness

top land/peak

pitch circle

dedendumcircle

root

pitchdiamete outside

diametebase

diamete

pitchliner

Parts of a Spur Gear

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J3103/2/18GEAR

1. Calculate the diameter of plug which will lie in the tooth space of a 5 mmmodule gear with its centre on the pitch circle. If the gear has 50T, find (a)

distance over two such plugs spaced in opposite spaces, (b) distance over twoplugs spaced 12 spaces apart (y = 20o)

2. Determine the diameter of a plug which will rest in the tooth space of a 4 mmmodule 20o rack, and touch the teeth at the pitch line. Calculate (a) the distanceover two such plugs spaced 5 teeth apart. (b) The depth from the top of the plugto the top of the teeth.

SELF-ASSESSMENT 2

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J3103/2/19GEAR

1. 7.38 mm (a) 257.38 mm (b) 178.52 mm

2. 5.9 mm (a) 59 mm (b) 10.664 mm

FEEDBACK OF SELF-ASSESSMENT 3

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