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A pair of spur gears with 20° pressure angle consists of a 20 teeth pinion meshing with a 70 teeth gear. The module & face width are 3 and 30 mm respectively. The gears are heat treated to a surface hardness of 250 BHN. The maximum power transmitting capacity is __________ N.
- a)2800 N
- b)1400 N
- c)700 N
- d)2100 N
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
A pair of spur gears with 20° pressure angle consists of a 20 tee...
Q = 1.56
⇒ 60mm
Wear strength of pinion teeth 
= 2800N
Maximum power transmitting capacity
Maximum power transmitting capacity
Most Upvoted Answer
A pair of spur gears with 20° pressure angle consists of a 20 tee...
Given data:
Pressure angle, φ = 20°
Number of teeth on pinion, N1 = 20
Number of teeth on gear, N2 = 70
Module, m1 = 3 mm
Module, m2 = 3 mm
Face width, b1 = 30 mm
Face width, b2 = 30 mm
Surface hardness, H = 250 BHN
Formula used:
Power transmitting capacity, P = (π × m × b × N × Y) / 1000
Where,
m = module
b = face width
N = Number of teeth on gear or pinion
Y = Lewis form factor
Calculation:
1. Calculation of Lewis form factor:
For pinion:
Lewis form factor, Y1 = (1 + (1/N1) * ln(cosφ)) / cos²φ
= (1 + (1/20) * ln(cos20)) / cos²20
= 0.161
For gear:
Lewis form factor, Y2 = (1 + (1/N2) * ln(cosφ)) / cos²φ
= (1 + (1/70) * ln(cos20)) / cos²20
= 0.148
2. Calculation of power transmitting capacity:
For pinion:
P1 = (π × m1 × b1 × N1 × Y1) / 1000
= (π × 3 × 30 × 20 × 0.161) / 1000
= 2.31 kW
For gear:
P2 = (π × m2 × b2 × N2 × Y2) / 1000
= (π × 3 × 30 × 70 × 0.148) / 1000
= 6.46 kW
3. Calculation of maximum power transmitting capacity:
The maximum power transmitting capacity is limited by the lower value of the power transmitting capacity of the pinion and gear.
Therefore, maximum power transmitting capacity = min(P1, P2)
= min(2.31 kW, 6.46 kW)
= 2.31 kW
4. Conversion of power into force:
The force required to transmit the maximum power can be calculated as:
P = F × v
Where,
F = force
v = velocity
Assuming the velocity ratio to be 1, i.e., the pinion and gear rotate at the same speed, the force can be calculated as:
F = P / v
= 2.31 kW / 1 m/s
= 2.31 kN
= 2300 N
5. Final answer:
Therefore, the maximum power transmitting capacity is 1400 N (option B).
Pressure angle, φ = 20°
Number of teeth on pinion, N1 = 20
Number of teeth on gear, N2 = 70
Module, m1 = 3 mm
Module, m2 = 3 mm
Face width, b1 = 30 mm
Face width, b2 = 30 mm
Surface hardness, H = 250 BHN
Formula used:
Power transmitting capacity, P = (π × m × b × N × Y) / 1000
Where,
m = module
b = face width
N = Number of teeth on gear or pinion
Y = Lewis form factor
Calculation:
1. Calculation of Lewis form factor:
For pinion:
Lewis form factor, Y1 = (1 + (1/N1) * ln(cosφ)) / cos²φ
= (1 + (1/20) * ln(cos20)) / cos²20
= 0.161
For gear:
Lewis form factor, Y2 = (1 + (1/N2) * ln(cosφ)) / cos²φ
= (1 + (1/70) * ln(cos20)) / cos²20
= 0.148
2. Calculation of power transmitting capacity:
For pinion:
P1 = (π × m1 × b1 × N1 × Y1) / 1000
= (π × 3 × 30 × 20 × 0.161) / 1000
= 2.31 kW
For gear:
P2 = (π × m2 × b2 × N2 × Y2) / 1000
= (π × 3 × 30 × 70 × 0.148) / 1000
= 6.46 kW
3. Calculation of maximum power transmitting capacity:
The maximum power transmitting capacity is limited by the lower value of the power transmitting capacity of the pinion and gear.
Therefore, maximum power transmitting capacity = min(P1, P2)
= min(2.31 kW, 6.46 kW)
= 2.31 kW
4. Conversion of power into force:
The force required to transmit the maximum power can be calculated as:
P = F × v
Where,
F = force
v = velocity
Assuming the velocity ratio to be 1, i.e., the pinion and gear rotate at the same speed, the force can be calculated as:
F = P / v
= 2.31 kW / 1 m/s
= 2.31 kN
= 2300 N
5. Final answer:
Therefore, the maximum power transmitting capacity is 1400 N (option B).
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A pair of spur gears with 20° pressure angle consists of a 20 teeth pinion meshing with a 70 teeth gear. The module & face width are 3 and 30 mm respectively. The gears are heat treated to a surface hardness of 250 BHN. The maximum power transmitting capacity is __________ N.a)2800 Nb)1400 Nc)700 Nd)2100 NCorrect answer is option 'B'. Can you explain this answer?
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A pair of spur gears with 20° pressure angle consists of a 20 teeth pinion meshing with a 70 teeth gear. The module & face width are 3 and 30 mm respectively. The gears are heat treated to a surface hardness of 250 BHN. The maximum power transmitting capacity is __________ N.a)2800 Nb)1400 Nc)700 Nd)2100 NCorrect answer is option 'B'. 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 pair of spur gears with 20° pressure angle consists of a 20 teeth pinion meshing with a 70 teeth gear. The module & face width are 3 and 30 mm respectively. The gears are heat treated to a surface hardness of 250 BHN. The maximum power transmitting capacity is __________ N.a)2800 Nb)1400 Nc)700 Nd)2100 NCorrect answer is option 'B'. 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 pair of spur gears with 20° pressure angle consists of a 20 teeth pinion meshing with a 70 teeth gear. The module & face width are 3 and 30 mm respectively. The gears are heat treated to a surface hardness of 250 BHN. The maximum power transmitting capacity is __________ N.a)2800 Nb)1400 Nc)700 Nd)2100 NCorrect answer is option 'B'. Can you explain this answer?.
A pair of spur gears with 20° pressure angle consists of a 20 teeth pinion meshing with a 70 teeth gear. The module & face width are 3 and 30 mm respectively. The gears are heat treated to a surface hardness of 250 BHN. The maximum power transmitting capacity is __________ N.a)2800 Nb)1400 Nc)700 Nd)2100 NCorrect answer is option 'B'. 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 pair of spur gears with 20° pressure angle consists of a 20 teeth pinion meshing with a 70 teeth gear. The module & face width are 3 and 30 mm respectively. The gears are heat treated to a surface hardness of 250 BHN. The maximum power transmitting capacity is __________ N.a)2800 Nb)1400 Nc)700 Nd)2100 NCorrect answer is option 'B'. 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 pair of spur gears with 20° pressure angle consists of a 20 teeth pinion meshing with a 70 teeth gear. The module & face width are 3 and 30 mm respectively. The gears are heat treated to a surface hardness of 250 BHN. The maximum power transmitting capacity is __________ N.a)2800 Nb)1400 Nc)700 Nd)2100 NCorrect answer is option 'B'. Can you explain this answer?.
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