Elongation of a Rotating bar
(Strength of Materials – by Er. R.K. Rajput)
ρ: density of the bar (kg/m3);
ω: angular velocity (rad/sec);
l: length of the bar (m);
E: Modulus of elasticity (N/m2)
The shafts that are connected in between two gears are subjected to vibration and deflections do take place when the critical velocity of the shaft is exceeded. At those times, the deflection produced by the shaft is to be calculated so that the stiffness value of the damper and the spring can be estimated and added to the system to maintain the mechanical equilibrium.
The above formula gives the relationship between the deflection, density, length, modulus of elasticity and the angular velocity of the bar.