Gears and Gearing Part 1 Types of Types of Gears

Spur Helical

Bevel Worm Nomenclature of Spur- Teeth

Fig. 13–5 Shigley’s Mechanical Engineering Design Rack

 A rack is a with an pitch diameter of infinity.  The sides of the teeth are straight lines making an angle to the line of centers equal to the pressure angle.

Fig. 13–13

Shigley’s Mechanical Engineering Design Tooth Size, Diameter, Number of Teeth

Shigley’s Mechanical Engineering Design Tooth Sizes in General Industrial Use

Table 13–2

Shigley’s Mechanical Engineering Design How an Involute Gear Profile is constructed

A1B1=A1A0, A2B2=2 A1A0 , etc Pressure Angle Φ has the values of 20° or 25 ° 14.5 ° has also been used. Gear profile is constructed from the base circle. Then additional clearance are given.

Relation of Base Circle to Pressure Angle

Fig. 13–10 Shigley’s Mechanical Engineering Design Standardized Tooth Systems: AGMA Standard

 Common pressure angles f : 20º and 25º  Older pressure angle: 14 ½º  Common face width: 35p F p  p  P 35 F PP

Shigley’s Mechanical Engineering Design Gear Sources

• Boston Gear • Martin • W. M. Berg • Stock Drive Products …. Numerous others

Shigley’s Mechanical Engineering Design Conjugate Action

 When surfaces roll/slide against each other and produce constant angular velocity ratio, they are said to have conjugate action.  Can be accomplished if instant center of velocity between the two bodies remains stationary between the grounded instant centers.

Fig. 13–6

Shigley’s Mechanical Engineering Design Fundamental Law of Gearing:

The common normal of the tooth profiles at all points within the mesh must always pass through a fixed point on the line of the centers called pitch point. Then the gearset’s velocity ratio will be constant through the mesh and be equal to the ratio of the gear radii.

Shigley’s Mechanical Engineering Design Conjugate Action: Fundamental Law of Gearing

 Forces are transmitted on line of action which is normal to the contacting surfaces.

 Velocity. VP of both gears is the same at point P, the pitch point VP  Angular velocity ratio is inversely proportional to the radii to point P, the pitch point.

 Circles drawn through P from each fixed pivot are pitch circles, each with a pitch radius.

Fig. 13–6

Shigley’s Mechanical Engineering Design

Gear Ratio

VP of both gears is the same at point P, the pitch (circle contact) point

푉푃 = 휔1푟1=휔2푟2 Gear Ratio >1 휔 푟 푁 1 = 2 = 2 휔2 푟1 푁1

ω2

ω2 rotates opposite of ω1

r1 P r2 ω 1 Pitch Circle of Gears

N1 N2 Nomenclature

Smaller Gear is and Larger one is the gear In most application the pinion is the driver, This reduces speed but it increases torque. Simple Gear Trains

 For a pinion 2 driving a gear 3, the speed of the driven gear is

VP

n3 =ω3 r2

P r3 n2 =ω2

N2 N3

Shigley’s Mechanical Engineering Design Simple Gear Trains (Gear 2 to Gear 4)

Fig. 13–27

Shigley’s Mechanical Engineering Design Compound

 A practical limit on train value for one pair of gears is 10 to 1  To obtain more, compound two gears onto the same shaft

Fig. 13–28

Shigley’s Mechanical Engineering Design Compound Gear Trains

n N N N 5  ( 1 )( 3 )( 4 ) n1 N 2 N 4 N5 Example 13–3

Shigley’s Mechanical Engineering Design Example 13–4

Shigley’s Mechanical Engineering Design Example 13–4

Shigley’s Mechanical Engineering Design Example 13–5

Shigley’s Mechanical Engineering Design Example 13–5

Shigley’s Mechanical Engineering Design Example 13–5

Shigley’s Mechanical Engineering Design Example 13–5

Shigley’s Mechanical Engineering Design Example 13–5

Shigley’s Mechanical Engineering Design