Unit2.doc

J3103/2/1 GEAR

UNIT 2

GEAR

OBJECTIVES

General Objective

: To understand the concept of gears and gearing

Specific Objectives

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

  

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

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INPUT

2.0

INTRODUCTION Gears are used to transmit power positively from one shaft to

another by means of successively engaging teeth (in two gears). They are used in place of belt drives and other forms of friction drive when exact speed ratios and power transmission must be maintained. Gears may also be used to increase or decrease the speed of the driven shaft, thus decreasing or increasing the torque of the driven number.

2.1. TYPES OF GEARS 2.1.1.

Spur gear

Spur gears, Fig. 2.1, are generally used to transmit power between two parallel shafts. The teeth on these gears are straight and parallel to the shafts to which they are attached.

When two

gears of different sizes are 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 are required.

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Gear

. Pinion

Figure 2.1. Spur gears 2.1.2.

Figure 2.2. Internal gears

Internal gears

Internal gears, Fig. 2.2., are used where the shafts are parallel and the centers must be closer together and that could be achieved with spur or 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 is required. 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 than intermittent action of the teeth, helical gears run more smoothly and quietly than spur gears. Since there is more than one tooth in engagement at any one time, helical gears are stronger than spur gears of the same size and pitch. However, special bearing (thrust bearings) are often required on shafts to overcome the end thrust produced by these gears as they turn.

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Figure 2.3. Helical gears 2.1.4.

Figure 2.4. Herringbone gears

Herringbone gears

Herringbone gears, Fig. 2.4., are resembles of two helical gears 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 continuous action and eliminate the need for thrust bearings. 2.1.5. Bevel gears When two shafts are located at an angle with their axial lines intersecting at 90o, power is generally transmitted by means of bevel gears, Fig. 2.5.

Figure 2.5. Bevel gears

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2.1.6.

Miter gears

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

Figure 2.6. Miter gears 2.1.7.

Figure 2.7. Angular bevel gears

Angular bevel gears

However, it is not necessary that the shafts be only at right angles in order to transmit power. If the axes of the shafts intersect at any angle other 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. The shafts of these gears, although at right angles, are not in the same plane and, therefore, do not intersect. Hypoid gears are used in automobile drives, Fig. 2.8.

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Worm

Worm gear

Figure 2.8. Hypoid gears 2.1.9.

Figure 2.9. Worm and worm gears

Worm and worm gear

When shafts are at right angles and considerable reduction in speed is 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 as fast 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, a rack and pinion may be used, Fig. 2.10. The rack, which is actually a straight or flat gear, may have straight teeth to mesh with a spur gear, or angular teeth to mesh with a helical gear.

Rack

Pinion J3103/2/7 GEAR

top land/peak

Fig. 2 face width root

addendum circle face

circular pitch thooth thickness

addendum

clearance

2.2.

Figure 2.10. Rack and pinion GEAR TERMINOLOGY

flank

pitch liner pitch circle

dedendum pitch diamete r

outside diamete r

base diamete r

dedendum circle

Fig. 2.11 Parts of a spur gear

2.2.1.

Addendum

Addendum is the radial distance between the pitch circle and the outside 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 bottom of the tooth space. 2.2.3.

Pitch diameter

J3103/2/8 GEAR

Pitch diameter is the diameter of the pitch circle which is equal to the outside diameter minus two addendums.

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 at the axis of the gear. 2.2.6.

Pitch line

The line formed by the intersection of the pitch surface and the tooth 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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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 measuring the pitch-line thickness of a tooth. It has two scales and must be set for the width (w) of the tooth, and the depth (h) from the top, at which the width occurs.

AO = R

Figure 2.12. The gear-tooth vernier caliper

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NOTE:

The following considerations of gear elements, the

symbols below will be used for the quantities. T/t

=

No. of teeth

P

=

Diametral pitch ( inch gear )

P

=

Circular pitch

D/d

=

Diameter of pitch circle

R/r

=

Radius of pitch circle



=

pressure angle

M

=

Modul

Add/A=

Addendum

Ded/D

=

Circular pitch

Dedendum =

 x Modul M

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

= AB =

1 360 90 x = ; T 4 T

T = no. of teeth

w 90 90 = AO sin = R sin T T 2

D

= Modul x No. of Teeth, and

R

=R

i.e.

MT 2

D = 2R =MT

and

R=

MT 2

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w MT 90 90 = R sin = sin T T 2 2

Hence

and

w = MT sin

90 T

(1)

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

OC = R + Add =

And

OB = R cos

Hence

h= =

MT +M 2

MT 90 90 = cos T T 2

MT MT 90 +M cos 2 2 T

MT MT 90 +M cos ] 2 2 T

=M+

MT 90 [ 1- cos ] 2 T

For diametral-pitch gears, (1) becomes w = And (2) becomes

(2)

h=

T 90 sin T P

1 T 90 [1+ ( 1 – cos ) T P 2

Example: To calculate the gear tooth vernier setting to measure a gear of 33T, 6 modul. w = MT sin

90 90 = 6 x 33 sin T 33

= 198 sin 2o 43.5’ = 198 x 0.0476 = 9.42 mm. h=

M[1+

T T ( 1 – cos )] 2 2

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=6[1+ =6[1+

33 90 ( 1 – cos )] 2 33 33 (0.0011) ] 2

= 6.11 mm

2.4.

PLUG METHOD OF CHECKING FOR PITCH DIAMETER AND DIVIDE OF TEETH The tooth vernier gives us a check on the size of the individual

tooth, but does not give a measure of either the pitch diameter or the accuracy of the division of the teeth.

Figure 2.13

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

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tooth as an empty space bounded by its outline, a circle with centre at O and radius OB would fit in the rack tooth and touch it at A and B (since OA and OB are 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 at points A and B and will have its centre on the pitch circle. In triangle OBD: OB = radius of plug required. OD = =

1 circular pitch 4

m 4

< B = 90o, < O =  OB = OD cos  =

m 4

cos 

Dia of plug = 2OD =

m 2

cos 

This is the diameter of a plug which will rest in the tooth space and have its centre on the pitch circle. Notice that the plug size remains the same for all gears having the same pitch and pressure angle. With such plugs placed in diametrically opposite tooth spaces, it is a simple 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:

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

Dia of plug = =

5 2

m 2

cos 

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)

Figure 2.14

Angle subtended by 10 teeth = 10 x

360 36

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= 100o.

In triangle OAB: AB = OA sin 50o = 90 x 0.766 = 68.94 Centre 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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ACTIVITY 2 2.1.

State three (3) characteristics of the following gears i. helical gear ii. spur gear

2.2.

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

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FEEDBACK ON ACTIVITY 2

2.1.

(a) 3 characteristics of helical gears; connect parallel shafts or shafts which are at an angle runs more smoothly and quietly than spur gears. gears are stronger than spur gears of the same size and pitch. (b) 3 characteristics of spur gears; i) ii) iii)

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. top land/peak face width root

addendum circle face

addendum

thooth thickness

clearance

circular pitch

flank

pitch liner pitch circle

dedendum pitch diamete r

outside diamete r

base diamete r

dedendum circle

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Parts of a Spur Gear

SELF-ASSESSMENT 2

1. Calculate the diameter of plug which will lie in the tooth space of a 5 mm module 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 two plugs spaced 12 spaces apart ( = 20o) 2. Determine the diameter of a plug which will rest in the tooth space of a 4 mm module 20o rack, and touch the teeth at the pitch line. Calculate (a) the distance over two such plugs spaced 5 teeth apart. (b) The depth from the top of the plug to the top of the teeth.

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FEEDBACK OF SELF-ASSESSMENT 3

1. 7.38 mm (a) 257.38 mm (b) 178.52 mm 2. 5.9 mm (a) 59 mm (b) 10.664 mm