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Homework Help: Design problem on a cement mixer

  1. Feb 24, 2010 #1
    1. The problem statement, all variables and given/known data

    Calculating torque on a portable cement mixer which is to be designed as a hollow cylinder with a closed base that rotates on a shaft (bearing). Dimentions being 0.5m diameter (D) and a height of 0.9m (h); the thickness of the cylinder is 0.006m (t). the drum is tilted at an angle of 15 degrees (@) to horizontal. it has aggregate of mass 363 kg (Ma) inside it. the drum operational speed is 10 rpm (sp). the drum is made of mild steel.


    2. Relevant equations
    Torque = moment of inertia * angular acceleration
    moment of inertia = mass * radius of gyration^2 (for hollow cylinder)
    F = mg
    density of mild steel (ds) = 7860 kg/m3
    final angular velocity = initial angular velocity + (angular acceleration * time)
    3. The attempt at a solution

    r = D/2
    volume of steel used on cylinder (Vc) = [(pi * r^2 * t)] + pi * [ {(r + t)^2} - (r^2)] * h
    mass of steel used on cylinder (Mc) = ds * Vc

    I = (Mc + Ma) * r^2

    assume it takes 2 second to reach speed of 10 rpm on start up

    angular acceleration (aa) = {[(sp * 2 * pi) /60] / 2}

    T = I * aa

    but i know the material in the cylinder will occupy a certain volume and have a centroid where the weigth will act, and where does the effect of the drum being tilted come into affect

    OR

    T = Fr
    F = (Mc + Ma) g
     
  2. jcsd
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