Numerical - Power transmitting capacity of gear box

Q.  A gear box having surface area of 0.30 m2 has overall heat transfer coefficient of 23 W/m2 oC,when a fan is mounted on worm shaft to circulate air on fins. What is the power transmitting capacity of a gear box based on thermal considerations, if temperature rise of lubricating oil is 50 oC? (Assume λ = 6o, Φn  = 22o & μ = 0.05)
- Published on 19 Oct 15

a. 1.023 kW
b. 1.006 kW
c. 1.227 kW
d. 2.000 kW

ANSWER: 1.006 kW

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    Discussion

  • Sravanthi   -Posted on 01 Oct 15
    Given: A = 0.30 m2 , C = 23 W/m2 oC, λ = 6o, Φn = 22o & μ = 0.05

    • Rate of heat generation = (1 – η) Pi
    • Rate of heat dissipation = CA Δt
    • Rate of heat generation is equal to rate of heat dissipation

    Therefore,

    Power transmitting capacity is given by
    (1 – η) Pi = CA Δt

    Formula: 1) (1 – η) Pi = CA Δt
    2) η = tan λ / tan ( Φv + λ)
    3) Φv = tan-1 ( μ / cos Φn)

    Substituting the given values we get,

    1) Φv = tan-1 ( μ / cos Φn )
    Φv = tan-1 ( 0.05 / cos 22)
    Φv = 3.086

    2) η = tan λ / tan ( Φv + λ)
    η = tan 6 / tan ( 3.086 + 6)
    η = 0.657

    Substituting the values of η = 0.657 and Φv = 3.086

    3) (1 – η) Pi = CA Δt
    (1 - 0.657) Pi = 23 x 0.30 x 50

    Therefore, Pi = 1.006 kW

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