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

Question

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.

Accepted Answer

A 90% force reduction corresponds to a transmissibility ratio of [latex]T_r[/latex] = 0.1. Using the approximate formula (13.2.13), we obtain

[latex]r^2=\frac{1 + T_r}{T_r}[/latex] (13.2.13)

[latex]r^2=\frac{1 + T_r}{T_r}=\frac{1.1}{0.1}=11[/latex]

From the definition of r and the fact that [latex]ω_n = \sqrt{k/m}[/latex], we have,

[latex]r^2=\frac{\omega^2}{\omega_n^2}=\omega^2 \frac{m}{k}[/latex]

Thus,

[latex]k=\frac{\omega^2}{r^2} m=\frac{[3200(2 \pi) / 60]^2}{11} \frac{10}{32.2}=3170 lb / ft[/latex]

Question 13.2.2: Often motors are mounted to a base with an isolator consisti......

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