Machine Design Miscellaneous
 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

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Lewis equation is given as
F = σ_{d} C_{v} bπ ym
F can be calculated as P / ωr ...[ω = 20 × 2π rad /sec]
D = mZ = 3 × 16 = 48mm
C_{v} = 1.5, b = 36, y = 0.3, m = 3∴ F = 3kW 40π 24 → 3 × 10^{3} × 10^{3} σ_{d} × 1.5 × 36 × π × 0.3 × 3 960 π
⇒ ω_{d}65 ≅ 65
⇒ nearest stress in gear tooth taking in account some F.O.S., σ = 58Correct Option: B
Lewis equation is given as
F = σ_{d} C_{v} bπ ym
F can be calculated as P / ωr ...[ω = 20 × 2π rad /sec]
D = mZ = 3 × 16 = 48mm
C_{v} = 1.5, b = 36, y = 0.3, m = 3∴ F = 3kW 40π 24 → 3 × 10^{3} × 10^{3} σ_{d} × 1.5 × 36 × π × 0.3 × 3 960 π
⇒ ω_{d}65 ≅ 65
⇒ nearest stress in gear tooth taking in account some F.O.S., σ = 58
 The resultant force on the contacting gear tooth is N is

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P = Tω
∴ 20 × 10^{3} =T.2π × 30
⇒ T =106. 1 Nm
Now, T = F_{t}. rHere, r = mTp = 5 × 20 = 50 nm = .05 m 2 2 F_{t} = 106.1 = 106.1 = 2122N r .05
∴ Resultant force,F = F_{t} = 2122 = 2258 N. cos θ cos 20°
Correct Option: C
P = Tω
∴ 20 × 10^{3} =T.2π × 30
⇒ T =106. 1 Nm
Now, T = F_{t}. rHere, r = mTp = 5 × 20 = 50 nm = .05 m 2 2 F_{t} = 106.1 = 106.1 = 2122N r .05
∴ Resultant force,F = F_{t} = 2122 = 2258 N. cos θ cos 20°
Direction: A gear set has a pinion with 20 teeth and a gear with 40 teeth. The pinion runs at 30 rev/s and transmits a power of 20 kW. The teeth are on the 20° fulldepth system and have a module of 5 mm. The length of the line of action is 19 mm.
 The contact ratio of the contacting tooth is

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Arc of contact (AOC) = 19 = 20.21 mm cos 20°
Circular pitch = πd = π m = π × 5 = 5πmm z Contact ratio = LOA = 20.21 = 1.29 Circular pitch 5.π
Correct Option: C
Arc of contact (AOC) = 19 = 20.21 mm cos 20°
Circular pitch = πd = π m = π × 5 = 5πmm z Contact ratio = LOA = 20.21 = 1.29 Circular pitch 5.π
 The center distance for the above gear set in mm is

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Centre distance
= m (T_{p} + T_{g}) = 5 (20 + 40) = 150 mm 2 2
Correct Option: B
Centre distance
= m (T_{p} + T_{g}) = 5 (20 + 40) = 150 mm 2 2
Direction: A 20° 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.
 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

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NA
Correct Option: B
NA