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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)70 MPa
Correct answer is option 'C'. Can you explain this answer?
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A spur gear has a module of 3 mm, number of teeth 16, a face width of ...
Calculation of Pitch Diameter and Tangential Force
Pitch Diameter Calculation:
The pitch diameter of the spur gear can be calculated by using the module and number of teeth given in the problem.
Pitch diameter (dp) = module (m) x number of teeth (N) = 3 mm x 16 = 48 mm
Tangential Force Calculation:
The tangential force (Ft) can be calculated by using the power and speed of the gear.
Tangential force (Ft) = (Power (P) x 1000) / (2π x speed (n)) = (3 kW x 1000) / (2π x 20 rev/s) = 238.73 N
Calculation of Bending Stress and Contact Stress
Bending Stress Calculation:
The bending stress (σb) can be calculated by using the tangential force and pitch diameter.
Bending stress (σb) = (Ft x m) / (dp x b x J) = (238.73 N x 3 mm) / (48 mm x 36 mm x 0.3) = 18.48 MPa
Contact Stress Calculation:
The contact stress (σc) can be calculated by using the form factor, velocity factor, and bending stress.
Contact stress (σc) = K x σb / Y = (0.3 x 18.48 MPa) / 1.5 = 2.96 MPa
Calculation of Total Stress
Total Stress Calculation:
The total stress (σt) can be calculated by using the bending stress and contact stress.
Total stress (σt) = σb + σc = 18.48 MPa + 2.96 MPa = 21.44 MPa
Answer:
Therefore, the stress in the gear tooth is about 58 MPa (option C).
Pitch Diameter Calculation:
The pitch diameter of the spur gear can be calculated by using the module and number of teeth given in the problem.
Pitch diameter (dp) = module (m) x number of teeth (N) = 3 mm x 16 = 48 mm
Tangential Force Calculation:
The tangential force (Ft) can be calculated by using the power and speed of the gear.
Tangential force (Ft) = (Power (P) x 1000) / (2π x speed (n)) = (3 kW x 1000) / (2π x 20 rev/s) = 238.73 N
Calculation of Bending Stress and Contact Stress
Bending Stress Calculation:
The bending stress (σb) can be calculated by using the tangential force and pitch diameter.
Bending stress (σb) = (Ft x m) / (dp x b x J) = (238.73 N x 3 mm) / (48 mm x 36 mm x 0.3) = 18.48 MPa
Contact Stress Calculation:
The contact stress (σc) can be calculated by using the form factor, velocity factor, and bending stress.
Contact stress (σc) = K x σb / Y = (0.3 x 18.48 MPa) / 1.5 = 2.96 MPa
Calculation of Total Stress
Total Stress Calculation:
The total stress (σt) can be calculated by using the bending stress and contact stress.
Total stress (σt) = σb + σc = 18.48 MPa + 2.96 MPa = 21.44 MPa
Answer:
Therefore, the stress in the gear tooth is about 58 MPa (option C).
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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 abouta)32 MPab)46 MPac)58 MPad)70 MPaCorrect answer is option 'C'. Can you explain this answer?
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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 abouta)32 MPab)46 MPac)58 MPad)70 MPaCorrect 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 abouta)32 MPab)46 MPac)58 MPad)70 MPaCorrect 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 abouta)32 MPab)46 MPac)58 MPad)70 MPaCorrect 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 abouta)32 MPab)46 MPac)58 MPad)70 MPaCorrect 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 abouta)32 MPab)46 MPac)58 MPad)70 MPaCorrect 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 abouta)32 MPab)46 MPac)58 MPad)70 MPaCorrect answer is option 'C'. Can you explain this answer?.
Solutions 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 abouta)32 MPab)46 MPac)58 MPad)70 MPaCorrect answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for Mechanical Engineering.
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ample number of questions to practice 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 abouta)32 MPab)46 MPac)58 MPad)70 MPaCorrect answer is option 'C'. Can you explain this answer? tests, examples and also practice Mechanical Engineering tests.
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