Each wheel of four wheeled rear engine automobile has a moment of inertia 2.4 Kg $m^2$ and an effective diameter of 660mm. The rotating parts of the engine have a moment of inertia of 1.2Kg $m^2$ . The gear ratio of engine to the back wheel is 3 to 1. The engine axis is parallel to the rear axle and the crankshaft rotates in the same sense as the road wheels. The mass of vehicle is 2200kg and the centre of the mass is 550mm above the road level. The track width of the vehicle is 1.5m. Determine the limiting speed of the vehicle around a curve with 80m radius so that all the four wheels maintain contact with the road surface. - Mumbai University > MECH > Sem 5 > Theory Of Machines 2

Marks: 10 M

Year: May 2015

Given:

$I_w = 2.4 kgm^2 \\ D=0.66m ; r= 0.33m \\ I_e= 1.2 kg m^2 \\ G = Ne/Nw = 3:1 = 3 \\ M = 2200kg; h = 0.55m \\ . a = 1.5m \\ R = 80m$

Solution:

For stability,

$V^2$ $≤ MgRa / 2(Mh + (4I_w + G I_e)/r) \\ ≤ 2200 \times 9.8 \times 80 \times 1.5 / 2 ( 2200 \times 0.55 + (4 \times 2.4 + 3 \times 1.2)/0.33)$

$V^2 ≤ 1034 \\ V ≤ 32.16 m/s \\ V ≤ 115.8 km/hr$