Question

C. An 80 mm long journal bearing supports a load of 2800 n on a 50 mm diameter shaft. The bearing has a radial clearance of 0.05 mm and the viscosity of the oil is 0.021kg/m-s at the operating temperature. If the bearing is capable of dissipating 80 j/s, determine the maximum safe speed.

Answer 1

Answer:

Explanation:

Answer for the given problem is provided in the image files attached. It is problem of sliding contact type bearing with assumption of steady state heat transfer.

Answer 2

Answer:

The maximum safe speed of the bearing $V=2.618 \times 10^{-3} \mathrm{~N}$

Explanation:

The maximum speed of a bearing is determined by its size and design. The higher the speed capability of a bearing, the smaller it is. Limiting speeds is influenced by a number of factors, including: Bearings with contact type seals have a much lower maximum speed when compared to open or non-contact sealed types.

Step 1 : In this question It's a sliding contact bearing problem with a steady-state heat transfer assumption

Length of journal bearing, $l=80 \mathrm{~mm}$

Load acting to the bearing, $L=2800 \mathrm{~N}$

Diameter of the shaft  $d=50 \mathrm{~mm}$

Partial clearance, $\frac{c}{2}=0.05$

$c=0.1 \mathrm{~mm}$

Viscosity of the oil, $Z=0.021 \mathrm{~kg} / \mathrm{ms}$

Heat dissipating capacity of bearing, $Q_{d}=80 \mathrm{~J} / \mathrm{s}$

Step2 :

Now load supporting of the bearing

$\begin{aligned}W &=p l d \\8800 &=p \times 80 \times 50 \\Q 800 &=p \times 4000 \\p &=0.7 \mathrm{~N} / \mathrm{mm}^{2}\end{aligned}$

Coefficient friction

$\begin{aligned}\mu &=\frac{33}{10^{8}}\left(\frac{Z N}{p}\right)\left(\frac{d}{c}\right]+0.002 \\&=\frac{33}{10^{8}}\left[\frac{0.021 \mathrm{~N}}{0.7}\right)\left[\frac{50}{0.1}\right]+0.002 \\&=\frac{33}{10^{8}} \times 0.03 \mathrm{~N} \times 500+0.002 \\\mu &=\frac{1}{10^{8}} \times 495 \mathrm{~N}+0.002\end{aligned}$

velocity of the shaft

$\begin{aligned}V &=\frac{\pi d N}{60} \\&=\frac{\pi \times 6.05 \times N}{60} \\V &=2.618 \times 10^{-3} \mathrm{~N}\end{aligned}$