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Prop Shaft load parked on a grade

  1. Nov 8, 2016 #1

    JGM

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    What would the torque on a driveshaft be for a 8 ton vehicle in park on a 16% grade? Tire radius is 19". Axle ratio it 7.1.
     
  2. jcsd
  3. Nov 8, 2016 #2

    berkeman

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    Staff: Mentor

    Welcome to the PF.

    Is this question for schoolwork? What is the context of the question?
     
  4. Nov 8, 2016 #3

    JGM

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    Trying to determine the loads on an output shaft of a transmission when parked on a grade with different axle ratios. Not for school work. Just general knowledge.
     
  5. Nov 8, 2016 #4

    jack action

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    If the rear wheels support the entire load caused by the slope, the force acting at the rear tires is ##F_w = W\sin\theta##, where ##W## is the weight of the vehicle and ##\theta## is the angle of the slope (reference). ##100\tan\theta = \%slope## to find the angle of the slope (reference).

    The wheel torque produced is ##T_w = F_w r##, where ##r## is the tire radius.

    The gear ratio reduces the torque seen by the driveshaft, so ##T_d = \frac{T_w}{GR}##, where ##GR## is the axle gear ratio.

    ##\theta = \arctan\frac{16}{100} = 9.1°##

    ##F_w = (16000\ lb)\sin9.1° = 2530\ lb##

    ##T_w = (2530.5\ lb) * (1.583\ ft) = 4006\ lb.ft##

    ##T_d = \frac{4006\ lb.ft}{7} = 572\ lb.ft##
     
  6. Nov 8, 2016 #5

    JGM

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    Shouldn't this include the acceleration of gravity?
    F_w = 16000 Lbs* 32.174 ft/s2
     
  7. Nov 8, 2016 #6

    pounds is a unit for weight not mass, already includes gravity.
     
  8. Nov 8, 2016 #7

    Baluncore

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    I used SI units.
    Mass = 8000 kg.
    Force due to gravity = 8000 * 9.8 = 78400 newton.
    Wheel radius is 39” = conveniently 1 metre.
    16% grade = 9.09 deg; Sin(9.09°) = 0.158
    7:1 axle ratio.
    Drive shaft torque = 1m * 78400N * 0.158 / 7 = 1769.5 Nm
    1769.5 Nm = 1305.1 ft.lbs
    This is quite different to jack action's 572. ft.lb
     
    Last edited: Nov 8, 2016
  9. Nov 8, 2016 #8

    jack action

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    That is because we don't use the same numbers:
    • I use 1 ton = 2000 lb and you use 1 tonne = 1000 kg;
    • I use a wheel radius of 19" and you use a wheel radius of 39".
    Other than that, everything is the same!:smile:
     
  10. Nov 8, 2016 #9

    Baluncore

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    Fixing the radius to 19” and using a mass of 8 Short Tons.
    Mass 8 short ton = 7257.5 kg.
    Force due to gravity = 7257.5 * 9.8 = 71123.5 newton.
    Wheel radius is 19” = inconveniently 0.4826 metre.
    16% grade = 9.09 deg; Sin(9.09°) = 0.158
    7:1 axle ratio.
    Drive shaft torque = 0.4826 * 71123.5 * 0.158 / 7 = 774.75 Nm
    774.75 Nm = 571.5 ft.lbs
    We agree.

    In Australia the standard Ton was a Long Ton = 1016.05 kg = 2240 lbs.
    In 1966 that was replaced by the metric Tonne = 1000 kg = 2205 lbs.

    Are vehicle weights in the USA always specified in Short Tons = 907.18 kg = 2000 lbs ?
     
  11. Nov 8, 2016 #10

    jack action

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    https://en.wikipedia.org/wiki/Short_ton

    I'm in Canada and a ton has always been 2000 lb around here. But we're with the SI system as well, so this is not a usual unit for us nowadays (unless we have to do business with our neighbor).

    As for truck classification, it is done in pounds, so no problem there:

    xskssrdsi0vac40ao6ij.jpg
     
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