Machine Design 3(2+1)

LESSON 22 GEARS

22.2   Types of Gears

Gears are broadly classified into following four groups:

Spur Gears: Spur gears have teeth parallel to the axis of rotation and are used for parallel shafts. These are the simplest type of gears. Spur gears impose radial loads on the shafts

Helical Gears: Helical gears are also used for parallel shafts. Teeth of helical gears are inclined to the axis of rotation. Due to gradual engagement of the teeth during meshing, these are less noisy in comparison to the spur gears. Inclined teeth develop axial thrust loads in addition to the radial loads. Sometimes helical gears are used to transmit motion between nonparallel shafts also.

Figure 22.1 Spur Gears

Figure 22.2 Helical Gears

 

Bevel Gears: have the shape of a truncated cone and are used to transmit power between intersecting shafts. Bevel gears can have straight or spiral teeth.

Worm Gears: Worm is in the form of a threaded screw which engages with a wheel. Axes of the two shafts are neither parallel nor intersecting and are generally at right angles to each other. Worm gears have very high reduction ratio.

 

Figure 22.3 Bevel Gears

     

 

Figure 22.4 Worm Gears

22.3   Gear Terminology

Important terms related to gears are discussed in Table 22.1 and are shown in Figure 22.5.

 

Figure 22.5 Gear Terminology

 

 Table 22.1 Gear Terminology

Pitch Surface	Surface of imaginary cylinders that roll together without slipping to give same motion as the actual gears
Pith Circle	It is the intersection of the pitch surface and a plane perpendicular to the axis of rotation
Pitch Circle Diameter	Diameter of the pitch circle
Pitch Point	Pitch circles of two mating gears are tangent to each other. The point of tangency where the two pitch circles meet is called pitch point
Base Circle	Circle from which the tooth profile curve is generated
Addendum Circle	Circle that bounds the outer ends of the teeth
Dedendum Circle	Circle that bounds the inner ends of the teeth
Addendum	Radial distance between the pitch circle and the addendum circle or height of the tooth above pitch circle
Dedendum	Radial distance between the pitch circle and the dedendum circle or depth of the tooth below pitch circle
Clearance	Amount by which Dedendum of a gear exceeds the addendum of the mating gear
Backlash	Amount by which width of a tooth space exceeds the thickness of mating tooth
Circular Pitch	Distance between two similar points on adjacent teeth measured along the pitch circle. It is given by, where d and Z are pitch circle diameter and number of teeth of the gear.
Diametral Pitch	Number of teeth per unit length of the pitch circle diameter and is given by,
Module	Ratio of pitch circle diameter to the number of teeth. It is given by,

 

 

22.4    Gear Profiles

Fundamental Law of Gearing states that common normal to the tooth profile at the point of contact should always pass through the pitch point. This law is satisfied by two curves – involute curve and cycloidal curve.

Cycloid is a curve traced by a point on the circumference of a circle which rolls without slipping on a fixed straight line. Curve traced by a point on the circumference of a circle which rolls without slipping on the outside of a fixed circle is called epicycloid and curve which rolls without slipping on the inside of a fixed circle is called hypercycloid. Involute is the curve traced by a point on a line that rolls on a circle without slipping.

Cycloidal teeth have epicycloid curve as their profile above the pitch circle and hypercycloid curve below the pitch circle. Combination of two curves makes the accurate manufacturing of cycloid tooth difficult. Also the pressure angle in case of cycloidal teeth doesn’t remain constant. Due to these disadvantages, cycloidal gears have become obsolete. Profile of involute teeth is made of a single curve, making it easier to manufacture. Also in case of the involute teeth pressure angle remains constant. Therefore involute teeth profile is mostly used in the gears.

22.5   Interference in Involute Gears

Involute profile is generated by the point on a line that rolls without slipping on a circle. Therefore the profile exists only outside this circle, called the base circle and portion of the gear tooth inside the base circle doesn’t follow the involute curve. The portion of the tooth outside base circle can be given any shape. But it is observed that if, for a given pressure angle, number of teeth on pinion are kept below certain value, this portion, which is not involute, comes in contact with the addendum of mating tooth. This is called interference. This can be avoided by providing undercuts on the pinion teeth but that decrease the strength of the gear tooth. Therefore to avoid interference minimum number of teeth are specified as given in the Table 22.2.

Table 22.2 Minimum Number of Teeth on Pinion to Avoid Interference

 

Gear Tooth System	Minimum Number of Teeth Required on Pinion
141/2° Full depth system	32
20° Full depth system	18
20° Stub system	14
141/2° Composite system	12

22.6   Backlash

It is the amount by which width of a tooth space exceeds the thickness of mating tooth. Backlash is intentionally provided to avoid jamming of the mating teeth, to compensate for machining errors and thermal expansion of teeth. Backlash can be provided by cutting the gears thinner or by slightly increasing the centre distance. This has no effect on the tooth action or velocity ratio. For gears to be used in precision equipment, backlash should be minimum.

22.7   Lubrication

Gears should be properly lubricated with a suitable lubricant for proper functioning and maximum life of the gears. Lubrication is required following purpose:

1. To reduce friction between rubbing tooth surfaces

2. To develop a fluid film between the tooth surfaces

3. To remove the heat generated due to functioning of gears and avoid overheating

4. To remove the abrasive particles from the tooth surfaces and reduce wear

5. Lubricant should be free from any debris, dirt or foreign particles and should be changed periodically.