150

QI = nondimensional inlet flow = 2qi/0.26 wRLc

QS = nondimensional side leakage flow = 2qs/0.26 wRLc

QI = nondimensional inlet flow = 2qi/0.26 wRLc

QS = nondimensional side leakage flow = 2qs/0.26 wRLc different LID ratios. If we assume that all the reference variables that go into the nondimensional parameters are identical, we can establish the following conclusions:

• The two-groove cylindrical hearing has the highest film thickness and thus the highest load capacity.

• The symmetric three-lobe bearing has the highest power loss.

• The canted three-lobe bearing has the greatest flow requirements.

Note that these comparisons were made on the basis of steady-state performances only. The major reason for applying lobe and tilting-pad bearings is to avoid dynamic instabilities.

Heat Balance Performance is based upon the assumption of a uniform viscosity in the fluid film. Since the viscosity is a strong function of temperature and since the temperature rise of the lubricant due to viscous heat generation is not known a priori, an iterative procedure is required to determine the average viscosity in the film. To determine an average viscosity, there must be a simplified heat balance in the film. The assumption is made that all the viscous heat generated in the film is absorbed by the lubricant as it flows through the film and produces a temperature rise.

FIGURE 18 Heat balance in a fluid film.

Figure 18 shows a developed view of the bearing surface and the parameters involved with conducting the heat balance. The lubricant enters a pad or bearing at the leading edge with an inlet flow qi and an inlet temperature t. As the lubricant enters the bearing surface and flows through it, the lubricant is exposed to a viscous shear, which adds heat to the fluid. In Figure 18, the viscous shear is indicated as a power input p. Some of the fluid flows out of the sides of the bearing, represented by qs/2, and some of the fluid, qc, is carried either over to the grooving of the next pad or back to the inlet groove for a single pad bearing.

Although the fluid temperature, and thus the viscosity, changes along the length of the pad, it is assumed that the temperature in the film increases to some value to for both the side leakage and carry-over fluids. Then the heat balance is conducted as follows: Heat added to a fluid by a viscous shear equals heat absorbed by the fluid.

Heat added to fluid by viscous shear = heat absorbed by fluid pJ = qsp€p(t0 - ti) = QcpCpito - ti) = (qs + Qc)pCp(to - ti) ()

qipCp where p = viscous heat generation, hp

J = heat equivalent constant = 0.7069 Btu/hp • s (J/kg • s) p = specific weight of flow, lb/in3 (kg/m3) Cp = specific heat of fluid, Btu/lb • °F(J/kg • °C) qi = bearing inlet flow, in3/s (mm3/s) At = temperature rise, °F(°C)

If qt is in gallons per minute [(1 in3/s = 0.26 gpm) = 16.39 cm3/s],

0.7069(0.26)p 0.1838p

qipCp qipCp

Before proceeding to a sample problem, a word about the flows qt and qs, and the general heat balance philosophy. The flow required by the bearing to prevent starvation is q;. The minimum make-up flow, or the flow that is lost from the ends of the bearing, is the side leakage qs. Theoretically then, the only flow that need be supplied to the bearing is qs. However, if this were true, then the heat balance formulation would require another balance between the carry-over flow qc at some temperature t0 and the make-up flow qs coming into the pad at temperature tt. It would be found that, if we supplied only qs to the bearing, excessive temperatures would result. In most instances, the amount of flow supplied to a bearing exceeds both the inlet flow and the side leakage flow by a significant margin. Designers often determine the flow to be supplied to a bearing system by a bulk temperature rise of the total flow entering the inlet pipe and exiting the exhaust pipe. Thus, the entire bearing is treated as a black box, and the total flow qT to the bearing system for a given bulk temperature rise At, is

Renewable Energy Eco Friendly

Renewable Energy Eco Friendly

Renewable energy is energy that is generated from sunlight, rain, tides, geothermal heat and wind. These sources are naturally and constantly replenished, which is why they are deemed as renewable.

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