gear trains
TRANSCRIPT
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
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
Contact Ratio
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
Primary Gear Characteristics
• Pressure angle/ tooth profile
• Face Width
• Gear ratio or number of teeth on both gears
• Centre to centre distance
• Module
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
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
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
Gear Trains
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4
4
3
2
1
1
5
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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
A
Arm
BO
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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
Planetary 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
Solution-1
Example-2
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
Thank you