EXAMPLE HYDRODYNAMIC BEARING

The similitude concept may be illustrated by considering an example. The problem of journal bearing load capacity is convenient for this purpose. In this problem, the minimum film thickness h) is related to a number of other variables, already defined in Ch. 5, Sec. 6.0 as follows  

Consider a prototype bearing having the following characteristics  

Journal diameter d) Diametral clearance (c) Bearing length ) Specific load (P) 

It is desired to test a I to 10 scale model in order to predict the minimum film thickness (h) from measurements on a model. In this problem, there are three dimensionally independent quantities and three arbitrary scale factors. One of these has already been fixed  

The corresponding dimensions for prototype and model are summarized in Table 7.1. 

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At this stage only measurements at the maximum load point have been recorded. The minimum film thickness in the bearing occurs at some position around the circumference in the direction of rotation. For this kind of steady state hydrodynamic bearing, lubricated with a Newtonian fluid, it is possible to determine the film thickness (and bearing attitude angle) for a numerical solution of Reynolds equation (see for example 7). Look-up tables and charts are available relating the Sommerfeld parameter to the bearing eccentricity ratio. 

Frankel and Acrivos11 have obtained models with well-defined hydrodynamics for very high concentrations of rigid and elastic particles. Here the solvent forms thin films and we enter the region of lubrication theory. The expressions describing the flow do bear some similarities to the semi-empirical expressions developed at lower concentrations. For example Frankel and Acrivos give... 

Various aspects of the hydrodynamics of gas-solid flnidization have been studied extensively with conclusions that afford guidance to the interpretation and extension of pilot plant data. Some of the leading results bearing on the sizing of vessels will be discussed here. Heat transfer performance is covered in Chapter 17. Example 6.16 applies to some of the cited data. 

In practical applications we often encounter a combination of boundary and hydrodynamic lubrication which is called mixed lubrication. For example, bearings that are usually lubricated hydrodynamically, experience mixed lubrication when starting and stopping. This is shown in the Stribeck diagram (Fig. 11.12) At low speeds, boundary lubrication with high friction... 

T.I.Fowle ° has pointed out the potential for molybdenum disulphide to reduce wire-wool failures of plain bearings. This type of failure can occur when a hardened adhesive wear particle becomes embedded in a relatively soft bush, causing severe abrasive wear of the counterface. The formation of the initial wear particle can arise from a transient failure of the hydrodynamic lubricant film, caused, for example by temporary interruption of a drip feed or coolant flow. Addition of a small amount of molybdenum disulphide, say 3% or more, to the lubricant can prevent the short-term occurrence of adhesive wear, and thus the formation of the initiating particle. 

Equation 2-15 is the Reynolds equation in two dimensions for the pressure p developed by hydrodynamic action in a film of incompressible fluid lubricant with no side leakage. The other variables are h, the film thickness, and x, the distance along the length of the bearing. For example, in Fig. 2-1 x is the distance along the circumference from the inlet to the outlet. 

RDE and RRDE are very convenient voltammetric methods for studying the mechanism and kinetics of ORR and are by far the most widely used methods. However, it is important to bear in mind that the underlying mathematical formulations of these methods are theorized for smooth electrode surfaces under laminar flow hydrodynamics. There are many examples in recent literature where RDE and RRDE have been used to study catalyst films for which turbulent flow hydrodynamics is quite obvious. The collection efficiency of RRDE for microscopically disordered films, for example, very porous materials and irregularly built-up films (as may be the case for catalysts modified with nanocarbons such as carbon nanotubes and graphenes), is likely to be determined erroneously due to sporadic hydrodynamics. Therefore, the quality of a given catalyst film has a great influence on the correctness of results obtained from RDE and RRDE. It is generally recommended that catalyst films for RDE and RRDE studies should be as thin as... 

In such a system, the coefficient of friction depends on the fluid dynamics, in particular on the viscosity r of the lubricant. For this reason, hydrodynamic lubrication is also called fluid lubrication. A well-known example of hydrodynamic lubrication is the effect of aquaplaning. When a car is driven at high speed on a wet road, the water forced between the surfaces of the tires cannot escape and separates the car from the road traction is lost. The build-up of the lubrication film either can be solely due to the relative movement of the bearing surfaces or can be achieved by active pumping of the lubricant (for a textbook, see Ref [954])... 

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