91Ó°ÊÓ

A machine is subjected to the vibration $$ x(t)=20 \sin 50 t+5 \sin 150 t \mathrm{~mm} \quad(t \text { in } \mathrm{s}) $$ An accelerometer having a damped natural frequency of \(80 \mathrm{rad} / \mathrm{s}\) and an undamped natural frequency of \(100 \mathrm{rad} / \mathrm{s}\) is mounted on the machine to read the acceleration directly in \(\mathrm{mm} / \mathrm{s}^{2}\). Discuss the accuracy of the recorded acceleration.

Two ball bearings, each with 16 balls, are used to support the shaft of a fan that rotates at 750 rpm. Determine the frequencies, in hertz, corresponding to the following defects: \(^{*}\) cage, inner race, outer race, and ball. Assume that \(d=15 \mathrm{~mm}, D=100 \mathrm{~mm}\), and \(\alpha=30^{\circ}\).

Determine the defect frequencies in hertz* corresponding to roller, inner race, outer race, and cage defects for a roller bearing with 18 rollers when installed in a machine that runs at a speed of \(1000 \mathrm{rpm}\). Assume \(d=2 \mathrm{~cm}, D=15 \mathrm{~cm},\) and \(\alpha=20^{\circ}\).

An angular contact thrust bearing consists of 18 balls, each of diameter \(10 \mathrm{~mm},\) and is mounted on a shaft that rotates at \(1500 \mathrm{rpm}\). If the contact angle of the bearing is \(40^{\circ}\) with a pitch diameter \(80 \mathrm{~mm}\), find the frequencies corresponding to cage, ball, inner race, and outer race faults.

Find the value of kurtosis for a vibration signal that is uniformly distributed in the range \(1-5 \mathrm{~mm}\) $$ f(x)=\frac{1}{4} ; \quad 1 \leq x \leq 5 \mathrm{~mm} $$