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Chapter 13: Problem 21

A journal bearing \(120 \mathrm{~mm}\) in diameter and \(60 \mathrm{~mm}\) long has a diametral clearance of \(0.20 \mathrm{~mm}\). The journal rotates \(3000 \mathrm{rpm}\) and is lubricated with SAE 20 oil at an average temperature of \(70^{\circ} \mathrm{C}\). Using Petroff's equation, estimate the power loss and the friction torque.

Short Answer

Expert verified
The estimated power loss is \(2.04 \, \text{kW}\) and the friction torque is \(6.497 \, \text{N.m}\).

Step by step solution

01

Finding Out the Values of Different Variables

The first step involves calculating the relevant parameters. The journal bearing diameter is \(d = 120 \, \text{mm}\), the length \(l = 60 \, \text{mm}\), the diametral clearance \(c = 0.20 \, \text{mm}\), the rotation speed \(N = 3000 \, \text{rpm}\), and the oil viscosity is estimated to be approximately \(0.029 \, \text{Pas}\) for SAE 20 oil at \(70^{\circ}C\). Now, it is needed to convert the diameter and clearance to meters for future calculations, so \(d = 0.12 \, \text{m}\), \(l = 0.06 \, \text{m}\), \(c = 0.00020 \, \text{m}\). The radius \(r = d/2 = 0.06 \, \text{m}\), and the angular speed \(\omega = 2 \pi N / 60 = 314.16 \, \text{rad/s}\).
02

Calculating Friction Torque Using Petroff's Equation

Now, use the Petroff's equation which is given by \(T = \eta \omega r^2 l / c\). Substituting the values into the Petroff's equation, you get \(T = 0.029 \times 314.16 \times (0.06)^2 \times 0.06 / 0.00020 = 6.497 \, \text{N.m}\). So the friction torque is \(6.497 \, \text{N.m}\).
03

Calculating Power Loss

The power loss in a bearing can be calculated using the equation \(P = T \omega\). Using the calculated friction torque and the angular speed, the power loss can be calculated as \(P = 6.497 \times 314.16 = 2040.9 \, \text{W}\) or \(2.04 \, \text{kW}\).

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Most popular questions from this chapter

Consult the Dodge bearing catalog for a sleeve bearing at http://dodge-pt.com/ literature/index.html and specify a two-bolt fully split housing pillow block bearing with bronze-bushed sleeve for a \(2.6875\)-in.-diameter steel shaft. Specify this bearing using the Dodge nomenclature key.

For SAE 20 oil at \(60^{\circ} \mathrm{F}\), determine the density in grams per cubic centimeter.

Consult the Dodge bearing catalog for a babbitted sleeve bearing at http://dodge-pt.com/ literature/index.html and specify a four-bolt pillow block babbitted angle bearing for a \(5.4375\)-in.-diameter steel shaft. Specify this bearing using the Dodge nomenclature key.

For the bearing specified in P13.3, consult the Dodge bearing catalog at http:// dodge-pt.com/literature/index.html and identify what take-up frame the specified bearing will fit and all the shaft sizes the take-up frame will accommodate. Specify the take-up frame size using the Dodge nomenclature.

A journal bearing of \(L=1 \mathrm{in} ., D=2 \mathrm{in.,}\) and a diametral clearance of \(0.002 \mathrm{in}\). supports a \(400-\mathrm{lb}\) load while rotating at \(1800 \mathrm{rpm}\). SAE 10 oil is used, with an average film temperature of \(130^{\circ} \mathrm{F}\). Determine (a) minimum oil film thickness, (b) coefficient of friction, (c) maximum film pressure, (d) angle between load direction and minimum film thickness, (e) angle between load direction and termination of film, (f) angle between load direction and maximum film pressure, (g) total circumferential oil flow rate, and (h) side or leakage flow rate. Would you recommend that a little smaller clearance or a little larger be used? Why?
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