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Two gears 40 and 30 involute teeth respectively are in mesh. Pressure angle = 20º, module pitch 12 mm. The length of contact on each side of the pitch point is half the maximum possible length. Find the height of addendum for each gear wheel.?
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Two gears 40 and 30 involute teeth respectively are in mesh. Pressure ...
Problem Statement:
Two gears with 40 and 30 teeth respectively are in mesh. The pressure angle is 20º and the module pitch is 12 mm. The length of contact on each side of the pitch point is half the maximum possible length. Find the height of addendum for each gear wheel.
Solution:
Step 1: Calculate the pitch diameter of each gear wheel.
Pitch diameter = number of teeth x module pitch
D1 = 40 x 12 = 480 mm
D2 = 30 x 12 = 360 mm
Step 2: Calculate the base diameter of each gear wheel.
Base diameter = pitch diameter x cos(pressure angle)
d1 = 480 x cos(20º) = 447.78 mm
d2 = 360 x cos(20º) = 335.83 mm
Step 3: Calculate the addendum height.
Addendum height = module pitch
h1 = h2 = 12 mm
Step 4: Calculate the maximum possible length of contact.
Maximum possible length of contact = 2 x √((r1 + h)^2 - (r2 + h)^2)
where r1 and r2 are the radii of the gear wheels, and h is the addendum height.
r1 = D1 / 2 = 240 mm
r2 = D2 / 2 = 180 mm
Maximum possible length of contact = 2 x √((240 + 12)^2 - (180 + 12)^2) = 101.60 mm
Step 5: Calculate the length of contact on each side of the pitch point.
Length of contact on each side of the pitch point = maximum possible length of contact / 2
= 101.60 / 2 = 50.80 mm
Step 6: Calculate the dedendum height.
Dedendum height = 1.25 x module pitch
= 1.25 x 12 = 15 mm
Therefore, the height of addendum for each gear wheel is 12 mm, and the length of contact on each side of the pitch point is 50.80 mm.
Two gears with 40 and 30 teeth respectively are in mesh. The pressure angle is 20º and the module pitch is 12 mm. The length of contact on each side of the pitch point is half the maximum possible length. Find the height of addendum for each gear wheel.
Solution:
Step 1: Calculate the pitch diameter of each gear wheel.
Pitch diameter = number of teeth x module pitch
D1 = 40 x 12 = 480 mm
D2 = 30 x 12 = 360 mm
Step 2: Calculate the base diameter of each gear wheel.
Base diameter = pitch diameter x cos(pressure angle)
d1 = 480 x cos(20º) = 447.78 mm
d2 = 360 x cos(20º) = 335.83 mm
Step 3: Calculate the addendum height.
Addendum height = module pitch
h1 = h2 = 12 mm
Step 4: Calculate the maximum possible length of contact.
Maximum possible length of contact = 2 x √((r1 + h)^2 - (r2 + h)^2)
where r1 and r2 are the radii of the gear wheels, and h is the addendum height.
r1 = D1 / 2 = 240 mm
r2 = D2 / 2 = 180 mm
Maximum possible length of contact = 2 x √((240 + 12)^2 - (180 + 12)^2) = 101.60 mm
Step 5: Calculate the length of contact on each side of the pitch point.
Length of contact on each side of the pitch point = maximum possible length of contact / 2
= 101.60 / 2 = 50.80 mm
Step 6: Calculate the dedendum height.
Dedendum height = 1.25 x module pitch
= 1.25 x 12 = 15 mm
Therefore, the height of addendum for each gear wheel is 12 mm, and the length of contact on each side of the pitch point is 50.80 mm.
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Two gears 40 and 30 involute teeth respectively are in mesh. Pressure angle = 20º, module pitch 12 mm. The length of contact on each side of the pitch point is half the maximum possible length. Find the height of addendum for each gear wheel.?
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Two gears 40 and 30 involute teeth respectively are in mesh. Pressure angle = 20º, module pitch 12 mm. The length of contact on each side of the pitch point is half the maximum possible length. Find the height of addendum for each gear wheel.? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about Two gears 40 and 30 involute teeth respectively are in mesh. Pressure angle = 20º, module pitch 12 mm. The length of contact on each side of the pitch point is half the maximum possible length. Find the height of addendum for each gear wheel.? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two gears 40 and 30 involute teeth respectively are in mesh. Pressure angle = 20º, module pitch 12 mm. The length of contact on each side of the pitch point is half the maximum possible length. Find the height of addendum for each gear wheel.?.
Two gears 40 and 30 involute teeth respectively are in mesh. Pressure angle = 20º, module pitch 12 mm. The length of contact on each side of the pitch point is half the maximum possible length. Find the height of addendum for each gear wheel.? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about Two gears 40 and 30 involute teeth respectively are in mesh. Pressure angle = 20º, module pitch 12 mm. The length of contact on each side of the pitch point is half the maximum possible length. Find the height of addendum for each gear wheel.? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two gears 40 and 30 involute teeth respectively are in mesh. Pressure angle = 20º, module pitch 12 mm. The length of contact on each side of the pitch point is half the maximum possible length. Find the height of addendum for each gear wheel.?.
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