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A spur gear has a module of 3 mm, number of teeth 16, a face width of 36 mm and a pressure angle of 20°. It is transmitting a power of 3 kW at 20 rev/s. Taking a velocity factor of 1.5, and a form factor of 0.3, the stress in the gear tooth is about
- a)32 MPa
- b)46 MPa
- c)58 MPa
- d)70MPa
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
A spur gear has a module of 3 mm, number of teeth 16, a face width of ...
To calculate the stress in the gear tooth, we need to consider several factors such as the power transmitted, the rotational speed, the gear parameters (module, number of teeth, face width), and the velocity factor and form factor.
1. Calculate the tangential force:
The power transmitted can be calculated using the formula:
Power (P) = Torque (T) x Angular velocity (ω)
Given:
Power (P) = 3 kW
Angular velocity (ω) = 20 rev/s
We can calculate the torque as follows:
T = P / ω
Substituting the given values:
T = 3 kW / 20 rev/s
Convert kW to W:
T = 3000 W / 20 rev/s
T = 150 Nm
The tangential force (Ft) can be calculated using the formula:
Ft = T / R
Where R is the pitch radius. Since module (m) and number of teeth (N) are given, we can calculate the pitch radius as follows:
Pitch radius (R) = m x N / 2
Given:
Module (m) = 3 mm
Number of teeth (N) = 16
Substituting the given values:
R = 3 mm x 16 / 2
R = 24 mm
Convert mm to meters:
R = 0.024 m
Substituting the values in the formula:
Ft = 150 Nm / 0.024 m
Ft = 6250 N
2. Calculate the bending stress:
The bending stress (σb) can be calculated using the formula:
σb = Ft / (m x b x Y)
Where b is the face width and Y is the combined effect of the velocity factor (Kv) and the form factor (Kf).
Given:
Face width (b) = 36 mm
Velocity factor (Kv) = 1.5
Form factor (Kf) = 0.3
Convert mm to meters:
b = 0.036 m
Substituting the values in the formula:
σb = 6250 N / (3 mm x 0.036 m x 1.5 x 0.3)
σb = 69444.44 N/m²
Convert N/m² to MPa:
σb = 69.44 MPa
3. Calculate the contact stress:
The contact stress (σc) can be calculated using the formula:
σc = Ft / (b x m x Z x Y)
Where Z is the number of teeth.
Substituting the values in the formula:
σc = 6250 N / (0.036 m x 3 mm x 16 x 1.5 x 0.3)
σc = 16203.7 N/m²
Convert N/m² to MPa:
σc = 16.2 MPa
4. Calculate the total stress:
The total stress (σ) can be calculated by adding the bending stress (σb) and the contact stress (σc):
σ = σb + σc
σ = 69.44 MPa + 16.2 MPa
σ ≈ 85.6 MPa
Therefore, the stress in the gear tooth is approximately 85.6 MPa. However, the closest answer choice provided is 58 MP
1. Calculate the tangential force:
The power transmitted can be calculated using the formula:
Power (P) = Torque (T) x Angular velocity (ω)
Given:
Power (P) = 3 kW
Angular velocity (ω) = 20 rev/s
We can calculate the torque as follows:
T = P / ω
Substituting the given values:
T = 3 kW / 20 rev/s
Convert kW to W:
T = 3000 W / 20 rev/s
T = 150 Nm
The tangential force (Ft) can be calculated using the formula:
Ft = T / R
Where R is the pitch radius. Since module (m) and number of teeth (N) are given, we can calculate the pitch radius as follows:
Pitch radius (R) = m x N / 2
Given:
Module (m) = 3 mm
Number of teeth (N) = 16
Substituting the given values:
R = 3 mm x 16 / 2
R = 24 mm
Convert mm to meters:
R = 0.024 m
Substituting the values in the formula:
Ft = 150 Nm / 0.024 m
Ft = 6250 N
2. Calculate the bending stress:
The bending stress (σb) can be calculated using the formula:
σb = Ft / (m x b x Y)
Where b is the face width and Y is the combined effect of the velocity factor (Kv) and the form factor (Kf).
Given:
Face width (b) = 36 mm
Velocity factor (Kv) = 1.5
Form factor (Kf) = 0.3
Convert mm to meters:
b = 0.036 m
Substituting the values in the formula:
σb = 6250 N / (3 mm x 0.036 m x 1.5 x 0.3)
σb = 69444.44 N/m²
Convert N/m² to MPa:
σb = 69.44 MPa
3. Calculate the contact stress:
The contact stress (σc) can be calculated using the formula:
σc = Ft / (b x m x Z x Y)
Where Z is the number of teeth.
Substituting the values in the formula:
σc = 6250 N / (0.036 m x 3 mm x 16 x 1.5 x 0.3)
σc = 16203.7 N/m²
Convert N/m² to MPa:
σc = 16.2 MPa
4. Calculate the total stress:
The total stress (σ) can be calculated by adding the bending stress (σb) and the contact stress (σc):
σ = σb + σc
σ = 69.44 MPa + 16.2 MPa
σ ≈ 85.6 MPa
Therefore, the stress in the gear tooth is approximately 85.6 MPa. However, the closest answer choice provided is 58 MP
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A spur gear has a module of 3 mm, number of teeth 16, a face width of ...
46 Mpa
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A spur gear has a module of 3 mm, number of teeth 16, a face width of 36 mm and a pressure angle of 20°. It is transmitting a power of 3 kW at 20 rev/s. Taking a velocity factor of 1.5, and a form factor of 0.3, the stress in the gear tooth is about a)32 MPa b)46 MPa c)58 MPa d)70MPa Correct answer is option 'C'. Can you explain this answer?
Question Description
A spur gear has a module of 3 mm, number of teeth 16, a face width of 36 mm and a pressure angle of 20°. It is transmitting a power of 3 kW at 20 rev/s. Taking a velocity factor of 1.5, and a form factor of 0.3, the stress in the gear tooth is about a)32 MPa b)46 MPa c)58 MPa d)70MPa Correct answer is option 'C'. 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 A spur gear has a module of 3 mm, number of teeth 16, a face width of 36 mm and a pressure angle of 20°. It is transmitting a power of 3 kW at 20 rev/s. Taking a velocity factor of 1.5, and a form factor of 0.3, the stress in the gear tooth is about a)32 MPa b)46 MPa c)58 MPa d)70MPa Correct answer is option 'C'. 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 A spur gear has a module of 3 mm, number of teeth 16, a face width of 36 mm and a pressure angle of 20°. It is transmitting a power of 3 kW at 20 rev/s. Taking a velocity factor of 1.5, and a form factor of 0.3, the stress in the gear tooth is about a)32 MPa b)46 MPa c)58 MPa d)70MPa Correct answer is option 'C'. Can you explain this answer?.
A spur gear has a module of 3 mm, number of teeth 16, a face width of 36 mm and a pressure angle of 20°. It is transmitting a power of 3 kW at 20 rev/s. Taking a velocity factor of 1.5, and a form factor of 0.3, the stress in the gear tooth is about a)32 MPa b)46 MPa c)58 MPa d)70MPa Correct answer is option 'C'. 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 A spur gear has a module of 3 mm, number of teeth 16, a face width of 36 mm and a pressure angle of 20°. It is transmitting a power of 3 kW at 20 rev/s. Taking a velocity factor of 1.5, and a form factor of 0.3, the stress in the gear tooth is about a)32 MPa b)46 MPa c)58 MPa d)70MPa Correct answer is option 'C'. 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 A spur gear has a module of 3 mm, number of teeth 16, a face width of 36 mm and a pressure angle of 20°. It is transmitting a power of 3 kW at 20 rev/s. Taking a velocity factor of 1.5, and a form factor of 0.3, the stress in the gear tooth is about a)32 MPa b)46 MPa c)58 MPa d)70MPa Correct answer is option 'C'. Can you explain this answer?.
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