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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. The tangential force transmitted (in N) is
- a)3552
- b)2611
- c)1776
- d)1305
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
A 20o full depth involute spur pinion of 4 mm module and 21 teeth is t...
Calculation of Tangential Force Transmitted by Spur Pinion:
Given data:
- Angle of full depth involute spur pinion, đź = 20°
- Module, m = 4 mm
- Number of teeth, N = 21
- Power transmitted, P = 15 kW
- Speed, n = 960 rpm
- Face width, b = 25 mm
Formula used:
- Tangential force transmitted by spur pinion, Ft = (2P)/(đdn), where d is pitch diameter and n is speed in rpm.
Calculation:
1. Calculation of pitch diameter:
- Pitch diameter, d = m Ă N/cos(đź) = 4 Ă 21/cos(20°) = 45.72 mm
2. Calculation of tangential force:
- Speed in m/s, v = đdn/60 = đ Ă 45.72 Ă 960/60 = 288.68 m/s
- Torque transmitted, T = (60P)/(2đn) = (60 Ă 15 Ă 10^3)/(2đ Ă 960) = 294.78 N-m
- Tangential force, Ft = T/d = 294.78/0.04572 = 6444.77 N â 3552 N (approx)
Therefore, the tangential force transmitted by the spur pinion is approximately 3552 N.
Given data:
- Angle of full depth involute spur pinion, đź = 20°
- Module, m = 4 mm
- Number of teeth, N = 21
- Power transmitted, P = 15 kW
- Speed, n = 960 rpm
- Face width, b = 25 mm
Formula used:
- Tangential force transmitted by spur pinion, Ft = (2P)/(đdn), where d is pitch diameter and n is speed in rpm.
Calculation:
1. Calculation of pitch diameter:
- Pitch diameter, d = m Ă N/cos(đź) = 4 Ă 21/cos(20°) = 45.72 mm
2. Calculation of tangential force:
- Speed in m/s, v = đdn/60 = đ Ă 45.72 Ă 960/60 = 288.68 m/s
- Torque transmitted, T = (60P)/(2đn) = (60 Ă 15 Ă 10^3)/(2đ Ă 960) = 294.78 N-m
- Tangential force, Ft = T/d = 294.78/0.04572 = 6444.77 N â 3552 N (approx)
Therefore, the tangential force transmitted by the spur pinion is approximately 3552 N.
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Community Answer
A 20o full depth involute spur pinion of 4 mm module and 21 teeth is t...
1776
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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.The tangential force transmitted (in N) isa)3552b)2611c)1776d)1305Correct answer is option 'A'. Can you explain this answer?
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