Chapter 10 Gears

Machines and Mechanisms: Applied Kinematic Analysis, 4/e

Chapter 10

Machines and Mechanisms: Applied Kinematic Analysis, 4/eDavid Myszka

© 2012, 2005, 2002, 1999 Pearson Higher Education,Upper Saddle River, NJ 07458. • All Rights Reserved.2



10.1 INTRODUCTION

Function of gears：

(1)Transmit motion from one shaft to another.(2)Increase or reduce speed, or change the direction of motion from one shaft to another.

Usually, the output speed of mechanical power source is much greater than the application requires. For example, the fax machine requires that the rollers feed the document at a compatibly low speed that that produced by a electric motor. Therefore, the speed must be reduced from the motor to the roller.



There are two standard methods to transmit the motion between shafts, gears and friction rollers/gears. To remedy the possibility of slipping, a gear is formed such that the smooth surfaces of the disks are replaced by teeth.



10.2 TYPES OF GEARS

(Annular)

Provide gradual engagement and produce less impact and noise.



10.2 TYPES OF GEARS



10.3 SPUR GEAR TERMINOLOGY

circular pitch

where pd is defined as diametral pitch and m is metric modulus



American standard



Metric (SI) standard



10.4 INVOLUTE TOOTH PROFILES

Basic requirement:A gear tooth must have a shape that keeps the driven gear rotating at a constant speed throughout the engagement and disengagement process.

2

3



Several forms of tooth shape have been identified as adequate candidates. However, of the possible shapes, only involute gear has becomes standard for most gear applications because of its excellent features.



10.5 STANDARD GEARS



10.6 RELATIONSHIPS OF GEARS IN MESH

10.6.1 Center Distance



10.6.2 Contact Ratio

Contact ratio is the average number of teeth that are in contact at any moment.



10.6.3 InterferenceThe most serious

drawback with using involute gear is the possibility of interference.

Interference is induced as the designers attempt to make gear assembly compact by using too few teeth on the gear.

When interference occurs, the face of the big gear interfere with the flank of the pinion.

Interference occurs when

where N1 and N2 are the numbers of the pinion and the gear

When a pinion meshes with a rack


© 2012, 2005, 2002, 1999 Pearson Higher Education,Upper Saddle River, NJ 07458. • All Rights Reserved.27Mechanics of Machines Cleghorn 27

For a given form of gear tooth, it is possible to determine the minimum number of teeth on a pinion that will mesh with a rack without requiring undercutting the pinion or removal of the addendum.

Therefore, However,

r

rKEsin

KEKE

/sin

r

Pk

r

a d

drP

k2sin

r

NPd 2

N

k2sin2

2sin

2kN

2sin



10.6.4 Undercutting



10.6.5 Backlash

Backlash is the amount that the width of the tooth space exceed the thickness of a gear tooth measured on the pitch circle.



10.6.6 Operating Pressure Angle



10.7 SPUR GEAR KINEMATICS

+ for internal gear- for external gears



10.8 SPUR GEAR SELECTION



10.8.3 Number of Teeth



10.9 RACK AND PINION KINEMATICS



10.10 HELICAL GEAR KINEMATICS (skiped to 10.13)



10.11 BEVEL GEAR KINEMATICS



10.12 WORM GEAR KINEMATICS



10.13 GEAR TRAINS

Train Value: When multiple gear pairs are used in a series, the overall velocity ratio is termed a “train value”.



10.14 IDLER GEARS



Question: Since idler gear has nothing to do with the train value, why they are still used?



10.15 PLANETARY GEAR TRAINS



Method 1: Tabular method



10.15.2 Planetary Gear Analysis by Equation

F: First gearL: Last gear



Method 2: Equation method

Chapter 10 Gears

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