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A 20o full depth involute spur pinion of 4 mm module and 21 teeth is to transmit 15 kW at 960 rpm. Its face width is 25 mm.
Q.
Given that the tooth geometry factor is 0.32 and the combined effect of dynamic load and allied factors intensifying the stress is 1.5; the minimum allowable stress (in MPa) for the gear material is
- a)242.0
- b)166.5
- c)121.0
- d)74.0
Correct answer is option 'B'. Can you explain this answer?
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Problem Statement: To find the minimum allowable stress for the gear material of a 20o full depth involute spur pinion.
Given data:
Module (m) = 4 mm
No. of teeth (N) = 21
Power transmitted (P) = 15 kW
Speed (N) = 960 rpm
Face width (b) = 25 mm
Tooth geometry factor (Y) = 0.32
Combined effect of dynamic load and allied factors intensifying the stress (K) = 1.5
Formula used:
Tangential force (Ft) = (2 × P × 10^3) / (π × N) ---(1)
Pitch diameter (D) = m × N ---(2)
Module factor (Km) = 1 ---(3)
Addendum (ha) = m ---(4)
Dedendum (hf) = 1.25 × m ---(5)
Tooth thickness (s) = π × m / 2 ---(6)
Contact ratio (C) = 1 ---(7)
Velocity factor (Kv) = 1 ---(8)
Dynamic factor (Kv) = ((C × Kv) / (C + Kv - 1))^(1/2) ---(9)
Dynamic load factor (Km) = 1 / (1 + Kf) ---(10)
Tooth load factor (Kf) = Y / (2 × Y - 1) ---(11)
Bending stress (σb) = (Ft × Km × Kv × Ks) / (b × m × Z × Y) ---(12)
Surface stress (σH) = Ft / (b × m × Y) ---(13)
Allowable bending stress (σba) = Sut / K ---(14)
Calculation:
Using equation (1), Ft = (2 × 15 × 10^3) / (π × 960) = 98.17 N
Using equation (2), D = 4 × 21 = 84 mm
Using equation (3), Km = 1
Using equation (4), ha = m = 4 mm
Using equation (5), hf = 1.25 × m = 5 mm
Using equation (6), s = π × m / 2 = 6.28 mm
Using equation (7), C = 1
Using equation (8), Kv = 1
Using equation (9), Kv = ((1 × 1) / (1 + 1 - 1))^(1/2) = 1
Using equation (11), Kf = Y / (2 × Y - 1) = 0.457
Using equation (10), Km = 1 / (1 + 0.457) = 0.686
Using equation (12), σb = (98.17 × 0.686 × 1 × 1) / (25 × 4 × 21 × 0.32) = 166.53 MPa
Using equation (13), σH = 98.17 / (25 × 4 × 0.32) = 30.58 MPa
Using equation (14), σba = Sut
Given data:
Module (m) = 4 mm
No. of teeth (N) = 21
Power transmitted (P) = 15 kW
Speed (N) = 960 rpm
Face width (b) = 25 mm
Tooth geometry factor (Y) = 0.32
Combined effect of dynamic load and allied factors intensifying the stress (K) = 1.5
Formula used:
Tangential force (Ft) = (2 × P × 10^3) / (π × N) ---(1)
Pitch diameter (D) = m × N ---(2)
Module factor (Km) = 1 ---(3)
Addendum (ha) = m ---(4)
Dedendum (hf) = 1.25 × m ---(5)
Tooth thickness (s) = π × m / 2 ---(6)
Contact ratio (C) = 1 ---(7)
Velocity factor (Kv) = 1 ---(8)
Dynamic factor (Kv) = ((C × Kv) / (C + Kv - 1))^(1/2) ---(9)
Dynamic load factor (Km) = 1 / (1 + Kf) ---(10)
Tooth load factor (Kf) = Y / (2 × Y - 1) ---(11)
Bending stress (σb) = (Ft × Km × Kv × Ks) / (b × m × Z × Y) ---(12)
Surface stress (σH) = Ft / (b × m × Y) ---(13)
Allowable bending stress (σba) = Sut / K ---(14)
Calculation:
Using equation (1), Ft = (2 × 15 × 10^3) / (π × 960) = 98.17 N
Using equation (2), D = 4 × 21 = 84 mm
Using equation (3), Km = 1
Using equation (4), ha = m = 4 mm
Using equation (5), hf = 1.25 × m = 5 mm
Using equation (6), s = π × m / 2 = 6.28 mm
Using equation (7), C = 1
Using equation (8), Kv = 1
Using equation (9), Kv = ((1 × 1) / (1 + 1 - 1))^(1/2) = 1
Using equation (11), Kf = Y / (2 × Y - 1) = 0.457
Using equation (10), Km = 1 / (1 + 0.457) = 0.686
Using equation (12), σb = (98.17 × 0.686 × 1 × 1) / (25 × 4 × 21 × 0.32) = 166.53 MPa
Using equation (13), σH = 98.17 / (25 × 4 × 0.32) = 30.58 MPa
Using equation (14), σba = Sut
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A 20o full depth involute spur pinion of 4 mm module and 21 teeth is to transmit 15 kW at 960 rpm. Its face width is 25 mm.Q.Given that the tooth geometry factor is 0.32 and the combined effect of dynamic load and allied factors intensifying the stress is 1.5; the minimum allowable stress (in MPa) for the gear material isa)242.0b)166.5c)121.0d)74.0Correct answer is option 'B'. Can you explain this answer?
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A 20o full depth involute spur pinion of 4 mm module and 21 teeth is to transmit 15 kW at 960 rpm. Its face width is 25 mm.Q.Given that the tooth geometry factor is 0.32 and the combined effect of dynamic load and allied factors intensifying the stress is 1.5; the minimum allowable stress (in MPa) for the gear material isa)242.0b)166.5c)121.0d)74.0Correct 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 20o full depth involute spur pinion of 4 mm module and 21 teeth is to transmit 15 kW at 960 rpm. Its face width is 25 mm.Q.Given that the tooth geometry factor is 0.32 and the combined effect of dynamic load and allied factors intensifying the stress is 1.5; the minimum allowable stress (in MPa) for the gear material isa)242.0b)166.5c)121.0d)74.0Correct 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 20o full depth involute spur pinion of 4 mm module and 21 teeth is to transmit 15 kW at 960 rpm. Its face width is 25 mm.Q.Given that the tooth geometry factor is 0.32 and the combined effect of dynamic load and allied factors intensifying the stress is 1.5; the minimum allowable stress (in MPa) for the gear material isa)242.0b)166.5c)121.0d)74.0Correct answer is option 'B'. Can you explain this answer?.
A 20o full depth involute spur pinion of 4 mm module and 21 teeth is to transmit 15 kW at 960 rpm. Its face width is 25 mm.Q.Given that the tooth geometry factor is 0.32 and the combined effect of dynamic load and allied factors intensifying the stress is 1.5; the minimum allowable stress (in MPa) for the gear material isa)242.0b)166.5c)121.0d)74.0Correct 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 20o full depth involute spur pinion of 4 mm module and 21 teeth is to transmit 15 kW at 960 rpm. Its face width is 25 mm.Q.Given that the tooth geometry factor is 0.32 and the combined effect of dynamic load and allied factors intensifying the stress is 1.5; the minimum allowable stress (in MPa) for the gear material isa)242.0b)166.5c)121.0d)74.0Correct 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 20o full depth involute spur pinion of 4 mm module and 21 teeth is to transmit 15 kW at 960 rpm. Its face width is 25 mm.Q.Given that the tooth geometry factor is 0.32 and the combined effect of dynamic load and allied factors intensifying the stress is 1.5; the minimum allowable stress (in MPa) for the gear material isa)242.0b)166.5c)121.0d)74.0Correct answer is option 'B'. Can you explain this answer?.
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