gear trains

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THOERY OF MECHANISMS AND MACHINES Gears Prepared by: Abhishek Attal Final Year Dual Degree Student Department of Mechanical Engineering Indian Institute of Technology Kanpur [email protected] NL-312

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Page 1: Gear Trains

THOERY OF MECHANISMS AND

MACHINESGears

Prepared by:

Abhishek AttalFinal Year Dual Degree Student

Department of Mechanical EngineeringIndian Institute of Technology Kanpur

[email protected] NL-312

Page 2: Gear Trains

Contact Ratio• To transmit rotational motion continuous there must be at least one pair of

contacting teeth at all times

• Typically, there are more than one pair in contact, hence overlapping of teeth

• Contact Ratio is used to provide quantitative measure of the amount of overlap

Page 3: Gear Trains

Contact Ratio

Page 4: Gear Trains

QuestionThe pitch circle radii of two involute spur gears in mesh are 51.5mm

and 64.2mm. The outer circle radii are 57.5mm and 71.2mm,

respectively, the operating pressure angle being 20 degrees.

Determine

1) Length of the path of contact

2) Contact ratio if the number of teeth on the larger gear is 20

Page 5: Gear Trains

Primary Gear Characteristics

• Pressure angle/ tooth profile

• Face Width

• Gear ratio or number of teeth on both gears

• Centre to centre distance

• Module

Page 6: Gear Trains

Gear Trains• Combination of gears that is used for transmitting motion from one shaft

to another is known as a Gear Train• Two or more gears working in a sequence (train) are called a gear train• Idler gear• A single idler gear is used to reverse the direction• Gear Trains 1. Simple gear train 2. Compound gear train 3. Epicyclic gear train

Page 7: Gear Trains

Simple Gear Train• Axes of rotation of each gear is fixed, each shaft has only one gear • Addition of each intermediate gear reverses direction of rotation of the final gear• In a sequence of gears chained together, the ratio depends only on the number of teeth on the first and last gear.• Consider gear train with 3 gears A,B,C. Let speed of rotation be , and , a and let number of teeth in each gear be , and

• The intermediate gears, regardless of their size, do not alter the overall gear ratio of the chain

Page 8: Gear Trains

Compound Gear Train• If any one of the intermediate shafts carries more

than one gear, then it is compound gear train

• Number of teeth on the intermediate gears will

influence the speed ratio

Page 9: Gear Trains

Gear Trains

))()((5

4

4

3

2

1

1

5

NN

NN

NN

nn

Page 10: Gear Trains

Epicyclic Gear Train• In epicyclic gear train one or more of the gear axes moves• Term epicyclic comes from the fact that points on gears with moving axes of rotation will describe epicycloid paths• Falkrik Wheel: Lifts boats in Scotland

Page 11: Gear Trains

A

Arm

BO

𝜃P

T

R

𝜃∅ S

Q

Analytical Method• Consider Simple Epicyclic gear train, where gear A can rotate about an arm

which itself rotates about the axis of gear B• Degree of Freedom of this System ??

• Consider , Arc RT = Arc RP • and are respective pitch diameters• Relative rotation of B with respect to arm = (CCW)• Relative rotation of A with respect to arm = (CW)

train value from A to B

Page 12: Gear Trains

Planetary Gear Trains

Page 13: Gear Trains

Example-1• A gearbox has an input speed of 1500 rev/min clockwise and an output speed of

300 rev/min anticlockwise. The input power is 20kW and the efficiency is 70%

• Determine the following

Gear Ratio

Input Torque

Output Power

Output Torque

Holding Torque

Page 14: Gear Trains

Solution-1

Page 15: Gear Trains

Example-2

Page 16: Gear Trains

Extras• Continuously variable transmission (CVT)• Internal and external gears• Harmonic gears- https://www.youtube.com/watch?v=bzRh672peNk• Falkrik Wheel (Boats lift in Scotland) https://

www.youtube.com/watch?v=k27gOmrDgpo• Involute Gear Profile https://www.youtube.com/watch?v=4QM0juVXW54• Involute Gear profile Draw https://www.youtube.com/watch?v=3bkw7C5z60E• Differential https://www.youtube.com/watch?v=yYAw79386WI• Compound Gear Train http://www.technologystudent.com/gears1/gears3.htm

Page 17: Gear Trains

Thank you