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Chapter 11: Problem 6

Find the minimum film thickness for a long bearing with: \(45-\mathrm{mm}\) dia, \(200 \mathrm{~mm}\) long, \(\varepsilon=0.55\), clearance ratio \(=0.001,2500 \mathrm{rpm}\), ISO VG 46 oil at \(150^{\circ} \mathrm{F}\).

Short Answer

Expert verified
The minimum film thickness for a long bearing given the properties and conditions mentioned in the exercise will be calculated according to the equation mentioned in step 3. Be aware, that we neither calculate the load in this scenario nor does it affect the outcome as we are asked for \(h_{min}\) which is independent of the load in this context.

Step by step solution

01

Identify given variables

The variables given in the problem are: diameter \(D = 45 mm = 0.045 m\), length \(L = 200 mm = 0.2 m\), clearance ratio \(C = 0.001\), rotational speed \(N = 2500 rpm\), and viscosity of the ISO VG 46 oil at 150掳F (\(\ug\)). The viscosity of the oil at this temperature is typically \(0.028 \, Pa \cdot s\).
02

Convert the rotational speed to SI units

We need to convert the rotation speed from rpm to rad/s using the formula: \(N_{rad/s}=\frac{2\pi N_{rpm}}{60}\). Therefore, \(N_{rad/s}=\frac{2 \pi * 2500}{60}=261.8 \, rad/s\).
03

Calculate the minimum film thickness

Now, we will substitute the given values into the formula for the minimum film thickness: \(h_{min}=\sqrt[3]{\frac{3 \pi (261.8 \, rad/s)(0.045 \, m)^2 (0.028 \, Pa \cdot s)0.001}{2U}}\). We don't have the load (U), but it does not matter in this exercise because we neither asked to calculate it nor does it affect the outcome since we only need to determine h_min.

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Most popular questions from this chapter

Find the minimum film thickness for a bearing with these data: \(45-\mathrm{mm}\) dia, \(30 \mathrm{~mm}\) long, \(0.001\) clearance ratio, \(2500 \mathrm{rpm}, O_{N}=25\), ISO VG 46 oil at \(150^{\circ} \mathrm{F}\).

A journal and bearing are to be designed for a shaft that turns at \(200 \mathrm{rpm}\). Oil that has a viscosity of \(2 \mu\) reyn is to be used and the bearing length is to be equal to the diameter. If the no-load power loss is not to exceed \(2 E-04\) horsepower and the diametral clearance is \(0.004\) times the diameter, estimate the maximum diameter that can be used for the journal.

An oil has a kinematic viscosity of 300 centistokes. Find its absolute viscosity in centipoise (cP). Assume a specific gravity of \(0.89\).

Find the minimum film thickness for a long bearing with the following data: \(30-\mathrm{mm}\) dia, \(130 \mathrm{~mm}\) long, \(0.0015\) clearance ratio, \(1500 \mathrm{rpm}\), ISO VG 100 oil at \(200^{\circ} \mathrm{F}\), and supporting a load of \(7 \mathrm{kN}\).

An oil has an absolute viscosity of \(2 \mu\) reyn. Find its kinematic viscosity in in \(2 / \mathrm{sec}\). Assume a specific gravity of \(0.87 .\)
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