Question 13.2.2: Isolation of a Motor Often motors are mounted to a base with...
Isolation of a Motor
Often motors are mounted to a base with an isolator consisting of an elastic pad. The pad serves to reduce the motor’s rotating unbalance force transmitted to the base. A particular motor weighs 10 lb and runs at 3200 rpm. Neglect damping in the pad and calculate the pad stiffness required to provide a 90% reduction in the force transmitted from the motor to the base.
A 90% force reduction corresponds to a transmissibility ratio of T_{r} = 0.1. Using the approximate formula (13.2.13), we obtain
r^{2} = \frac{1 + T_{r}}{T_{r}} = \frac{1.1}{0.1} = 11
From the definition of r and the fact that ω_{n} = \sqrt{k/m}, we have,
r^{2} = \frac{ω^{2}}{ω^{2}_{n}} = ω^{2} \frac{m}{k}
Thus,
k = \frac{ω^{2}}{r^{2}} m = \frac{[3200(2π)/60]^{2}}{11} \frac{10}{32.2} = 3170 lb/ft