Answer to Question #123436 in Mechanical Engineering for A

Question

The stroke of a steam engine is 600 mm and the length of connecting rod is 1.5 m. The crank rotates at 180 r.p.m. Determine: 1. velocity and acceleration of the piston when crank has travelled through an angle of 40° from inner dead centre, and 2. the position of the crank for zero acceleration of the piston.

Answer 1

Given,

stroke of the steam engine r = 0.6m

length of the connecting rod l = 1.5m

speed of the crank N = 180 rpm

n = l/r = 1.5/0.6 = 2.5

a) velocity of the piston at angle = 40⁰ is

v = l (1/square root 1-(sin thita/n)² * (r/l)² 2sin thita cos thita *w +rsin thita *w

v = 1.5 (1/square root 1-(sin 40⁰/2.5)² *(0.6/1.5)² 2sin40⁰ cos40⁰*18.84 +0.6 sin 40⁰ *18.84

v = 6.217m/s

acceleration of the piston is given by

a = w²r (cos thita + cos 2 thita/n)

a = 18.84² * 0.6 ( cos 40⁰ + cos 2 (40⁰)/2.5 )

a = 9.44 m²/sec

b) position of the crank when the acceleration is zero

a = w²r (cos thita + cos 2 thita/n)

thita = 18.84² *0.6 ( cos thita + cos 2 thita /2.5)

thita = 71.40⁰