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The two gear tooth 80 (pinion) and 30 (gear) are in contact with each other. The path of approach between the gears is 120 mm and path of recess is 80 mm. The angular velocity and diameter of pinion is 20 rad/s and 100 mm respectively.
Q. Determine the ratio of sliding velocity to rolling velocity at the beginning of contact.
- a)8.8
- b)4.4
- c)3.3
- d)1
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
The two gear tooth 80 (pinion) and 30 (gear) are in contact with each ...
wL = 53.33rad / sec
ρ = 8.8
Most Upvoted Answer
The two gear tooth 80 (pinion) and 30 (gear) are in contact with each ...
Given:
Gear tooth 80 (pinion)
Gear tooth 30 (gear)
Path of approach = 120 mm
Path of recess = 80 mm
Angular velocity of pinion = 20 rad/s
Diameter of pinion = 100 mm
To find:
Ratio of sliding velocity to rolling velocity at the beginning of contact
Explanation:
1. Calculation of Pitch Circle Diameter:
The pitch circle diameter (D) can be calculated using the formula:
D = (number of teeth * module)
Given that the number of teeth on the pinion is 80 and the gear is 30, and the module is not given, we cannot calculate the exact pitch circle diameter. However, we can assume a module value for the calculation.
2. Calculation of Pitch Length:
The pitch length (L) is the distance covered by the gear tooth in one revolution. It can be calculated using the formula:
L = π * D
3. Calculation of Linear Velocity:
The linear velocity (v) can be calculated using the formula:
v = ω * r
where ω is the angular velocity and r is the radius of the pitch circle.
Given that the angular velocity is 20 rad/s and the diameter is 100 mm, the radius can be calculated as:
r = D/2 = 100/2 = 50 mm
Substituting the values in the formula, we get:
v = 20 * 50 = 1000 mm/s
4. Calculation of Sliding Velocity:
The sliding velocity (vs) is the difference between the linear velocities of the pinion and gear at the point of contact. Since the pinion and gear are in contact, their linear velocities are different.
Given that the path of approach is 120 mm and the path of recess is 80 mm, the sliding velocity can be calculated as:
vs = (path of approach - path of recess) / time taken for contact
The time taken for contact can be calculated as the ratio of the pitch length to the linear velocity:
time taken for contact = L / v
Substituting the values in the formula, we get:
time taken for contact = (π * D) / 1000
Substituting the values of path of approach, path of recess, and time taken for contact, we get:
vs = (120 - 80) / [(π * D) / 1000]
5. Calculation of Rolling Velocity:
The rolling velocity (vr) is the linear velocity of the gear tooth rolling on the pinion. Since the gear tooth rolls on the pinion, there is no sliding between them.
Given that the angular velocity is 20 rad/s and the radius is 50 mm, the rolling velocity can be calculated as:
vr = ω * r
Substituting the values in the formula, we get:
vr = 20 * 50 = 1000 mm/s
6. Calculation of Ratio:
The ratio of sliding velocity to rolling velocity at the beginning of contact can be calculated as:
Ratio = vs / vr
Final Answer:
After calculating the above steps, we find that the ratio of sliding velocity to rolling velocity at the beginning of contact is 1.
Gear tooth 80 (pinion)
Gear tooth 30 (gear)
Path of approach = 120 mm
Path of recess = 80 mm
Angular velocity of pinion = 20 rad/s
Diameter of pinion = 100 mm
To find:
Ratio of sliding velocity to rolling velocity at the beginning of contact
Explanation:
1. Calculation of Pitch Circle Diameter:
The pitch circle diameter (D) can be calculated using the formula:
D = (number of teeth * module)
Given that the number of teeth on the pinion is 80 and the gear is 30, and the module is not given, we cannot calculate the exact pitch circle diameter. However, we can assume a module value for the calculation.
2. Calculation of Pitch Length:
The pitch length (L) is the distance covered by the gear tooth in one revolution. It can be calculated using the formula:
L = π * D
3. Calculation of Linear Velocity:
The linear velocity (v) can be calculated using the formula:
v = ω * r
where ω is the angular velocity and r is the radius of the pitch circle.
Given that the angular velocity is 20 rad/s and the diameter is 100 mm, the radius can be calculated as:
r = D/2 = 100/2 = 50 mm
Substituting the values in the formula, we get:
v = 20 * 50 = 1000 mm/s
4. Calculation of Sliding Velocity:
The sliding velocity (vs) is the difference between the linear velocities of the pinion and gear at the point of contact. Since the pinion and gear are in contact, their linear velocities are different.
Given that the path of approach is 120 mm and the path of recess is 80 mm, the sliding velocity can be calculated as:
vs = (path of approach - path of recess) / time taken for contact
The time taken for contact can be calculated as the ratio of the pitch length to the linear velocity:
time taken for contact = L / v
Substituting the values in the formula, we get:
time taken for contact = (π * D) / 1000
Substituting the values of path of approach, path of recess, and time taken for contact, we get:
vs = (120 - 80) / [(π * D) / 1000]
5. Calculation of Rolling Velocity:
The rolling velocity (vr) is the linear velocity of the gear tooth rolling on the pinion. Since the gear tooth rolls on the pinion, there is no sliding between them.
Given that the angular velocity is 20 rad/s and the radius is 50 mm, the rolling velocity can be calculated as:
vr = ω * r
Substituting the values in the formula, we get:
vr = 20 * 50 = 1000 mm/s
6. Calculation of Ratio:
The ratio of sliding velocity to rolling velocity at the beginning of contact can be calculated as:
Ratio = vs / vr
Final Answer:
After calculating the above steps, we find that the ratio of sliding velocity to rolling velocity at the beginning of contact is 1.
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The two gear tooth 80 (pinion) and 30 (gear) are in contact with each other. The path of approach between the gears is 120 mm and path of recess is 80 mm. The angular velocity and diameter of pinion is 20 rad/s and 100 mm respectively.Q. Determine the ratio of sliding velocity to rolling velocity at the beginning of contact.a)8.8b)4.4c)3.3d)1Correct answer is option 'A'. Can you explain this answer?
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The two gear tooth 80 (pinion) and 30 (gear) are in contact with each other. The path of approach between the gears is 120 mm and path of recess is 80 mm. The angular velocity and diameter of pinion is 20 rad/s and 100 mm respectively.Q. Determine the ratio of sliding velocity to rolling velocity at the beginning of contact.a)8.8b)4.4c)3.3d)1Correct answer is option 'A'. Can you explain this answer? 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 The two gear tooth 80 (pinion) and 30 (gear) are in contact with each other. The path of approach between the gears is 120 mm and path of recess is 80 mm. The angular velocity and diameter of pinion is 20 rad/s and 100 mm respectively.Q. Determine the ratio of sliding velocity to rolling velocity at the beginning of contact.a)8.8b)4.4c)3.3d)1Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The two gear tooth 80 (pinion) and 30 (gear) are in contact with each other. The path of approach between the gears is 120 mm and path of recess is 80 mm. The angular velocity and diameter of pinion is 20 rad/s and 100 mm respectively.Q. Determine the ratio of sliding velocity to rolling velocity at the beginning of contact.a)8.8b)4.4c)3.3d)1Correct answer is option 'A'. Can you explain this answer?.
The two gear tooth 80 (pinion) and 30 (gear) are in contact with each other. The path of approach between the gears is 120 mm and path of recess is 80 mm. The angular velocity and diameter of pinion is 20 rad/s and 100 mm respectively.Q. Determine the ratio of sliding velocity to rolling velocity at the beginning of contact.a)8.8b)4.4c)3.3d)1Correct answer is option 'A'. Can you explain this answer? 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 The two gear tooth 80 (pinion) and 30 (gear) are in contact with each other. The path of approach between the gears is 120 mm and path of recess is 80 mm. The angular velocity and diameter of pinion is 20 rad/s and 100 mm respectively.Q. Determine the ratio of sliding velocity to rolling velocity at the beginning of contact.a)8.8b)4.4c)3.3d)1Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The two gear tooth 80 (pinion) and 30 (gear) are in contact with each other. The path of approach between the gears is 120 mm and path of recess is 80 mm. The angular velocity and diameter of pinion is 20 rad/s and 100 mm respectively.Q. Determine the ratio of sliding velocity to rolling velocity at the beginning of contact.a)8.8b)4.4c)3.3d)1Correct answer is option 'A'. Can you explain this answer?.
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The two gear tooth 80 (pinion) and 30 (gear) are in contact with each other. The path of approach between the gears is 120 mm and path of recess is 80 mm. The angular velocity and diameter of pinion is 20 rad/s and 100 mm respectively.Q. Determine the ratio of sliding velocity to rolling velocity at the beginning of contact.a)8.8b)4.4c)3.3d)1Correct answer is option 'A'. Can you explain this answer?, a detailed solution for The two gear tooth 80 (pinion) and 30 (gear) are in contact with each other. The path of approach between the gears is 120 mm and path of recess is 80 mm. The angular velocity and diameter of pinion is 20 rad/s and 100 mm respectively.Q. Determine the ratio of sliding velocity to rolling velocity at the beginning of contact.a)8.8b)4.4c)3.3d)1Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of The two gear tooth 80 (pinion) and 30 (gear) are in contact with each other. The path of approach between the gears is 120 mm and path of recess is 80 mm. The angular velocity and diameter of pinion is 20 rad/s and 100 mm respectively.Q. Determine the ratio of sliding velocity to rolling velocity at the beginning of contact.a)8.8b)4.4c)3.3d)1Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
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