A loaded porter governor has 4 links each 25cm long, 2 revolving masses each weighing 30N and a central dead weight weighing 200N. All the links are attached to respective sleeves at radial distances of 4 cm from the axis of rotation. The masses resolve at a radius of 15 cm at minimum speed and at a radius of 20 cm at maximum speed. Determine the range of the speed.

Mumbai University > Mechanical Engineering > Sem 5 > Theory of Machines-II

Marks: 10 Marks

Year: Dec 2015

1. 4 links = 25 cm = 250 mm

2. m = 30 N

   $w= m * g \\ m = 30/9.81 \\ m= 3.05 kg$

$ \begin{array} \ M &= 200 N \\ &= 200/ 9.81 \\ &= 20.38 kg \end{array} $

Calculation of minimum and maximum speed of the governor.

$h_1$ $=\sqrt{BP^2+BD^2} \\ = \sqrt{0.25^2+0.11^2} \\ = 0.2244 m$

Similarly for $h_2$

$h_2$ $=\sqrt{BP^2+BD^2} \\ = \sqrt{0.25^2+0.16^2} \\ =0.192 m$

We know that the arms are equal,

$N_1 ²$ $= [(m +M )* g *91.2 ]/m * h_1 \\ = [(3.05+20.38)*9.81*91.2]/3.05 * 0.2244 \\ = 30627$

$N_1 = 175.00$

$N_2 ²$ $= [(m +M )* g *91.2 ]/m * h_2 \\ = [(3.05+20.38)*9.81*91.2]/3.05 * 0.192 \\ N_2 =189.19$

Range of speed $= N_2 - N_1$ $=189.19 -175.00 \\ =14.198 rpm$