vb.net barcode reader code Fig 632: Waukesha whitemetal-lined in Software

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Fig 632: Waukesha whitemetal-lined
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bearing for a water turbine with directed lubrication [15]
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Fig 633: Waukesha silicon carbide thrust and journal
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bearings [15]
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Hydrodynamic thrust bearings are also used in reverse osmosis applications wherein the grease or oil is replaced with a process lubricant A tilting-pad design is chosen because it has a sufficient load capacity, compactness and efficiency FMC Technologies, Houston, uses the bearing shown in Figure 634 for such applications up to 5,000 hours without any sign of wear Several bearing manufacturers are currently testing various new materials, which can lead to hydrodynamic bearings having a better performance Waukesha, for instance, has found
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Fig 634: Waukesha HIPERAX thrust bearing with
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solid polymer pads [15]
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that polymer bearings provide an alternative in both oil-lubricated applications and those lubricated by a process fluid A polymer based on polyether-ether-ketone (PEEK), which combines excellent surface properties with a high working temperature, has been introduced Basically, this new range of polymer materials is capable of higher operating temperatures up to 250 C (480 F), high load capability, corrosion resistance and a high electrical resistivity (better than 109 m) [15]
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637 Mathematical Approximation of Hydrodynamic Bearings
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The analysis of hydrodynamic journal and thrust bearings is usually tedious and is fully dependent on the shape of the pad for thrust bearings The analysis involves the extensive use of the principles of fluid mechanics and derivation of Reynolds equation For journal bearings, several approximations may be applied such as the full Sommerfeld solution, half Sommerfeld solution and Reynolds Boundary condition For the purpose of introduction, these mathematical analyses are not included Reference can be made to the work of Hamrock titled Fundamentals of Fluid Film Lubrication [1] For certain applications, the operating temperature and the type of lubricant are crucial in determining the viscosity of the lubricant under consideration Figure 635 shows the viscositytemperature curves for typical SAE (Society of Automotive Engineers) numbered oils A simplified approach to obtain the friction of a hydrodynamic sliding journal bearing has been analysed by Petroff in whose equation the shaft is assumed to be concentric [13] This is only possible when the radial load action on the bearing is negligible, the viscosity of the lubricant is infinite and the speed of the journal is infinite This however is seldom possible Petroff s equation gives a good approximation even when the criteria are not fully satisfied By referring to a vertical shaft shown in Figure 636, it is assumed that there is no eccentricity between the bearing and the journal, and hence no wedging action and no lubricant flow in the axial direction [5] The absolute viscosity is given by =
Rearranging the previous equation, the friction force in a concentric journal bearing is then given as AU F= where F is the friction torque/shaft radius = Tf /RI, A, the pDL = 2pRL, U, the (pDn = 2pRn (n is in revolutions/sec, rps) and H is the c (c = radial clearance = (bearing diameter shaft diameter) 2) Substituting and solving for the friction torque gives Tf 2 RL2 Rn = R C 2 4 nLR 3 Tf = C
Fh AU
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Fig 635: Viscosity versus temperature curves for a typical SAE graded oil [4]
If a small radial load, W, is applied to the shaft, the frictional drag force can be considered equal to the product ( fW ) Thus, the friction torque can be expressed as Tf = f WR = f (DLP) R, where P is the radial load per unit of the projected bearing area, W = P/DL The imposition of load W will cause the shaft to become somewhat eccentric in the bearing Neglecting this effect and equating the two expressions for the friction torque will give Petroff s equation
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n R f = 2 2 P C This equation provides a quick and simple estimate of coefficients of friction of lightly loaded bearings Petroff s equation identifies two very important bearing parameters, the significance of n/P and the ratio R/C R/C is also known as the clearance ratio which ranges between 500 and 10,000 From the previous relations, the power loss can be calculated from Power loss (Watt) = 2pnTf
Example: Petroff s Bearing Analysis Estimate the bearing coefficient of friction and the power loss using Petroff s approach for the following given data [5]: Shaft diameter, D = 100 mm Bearing length, L = 80 mm Diametrical clearance, c = 010 mm Oil viscosity, = 50 mPasec Rotational speed, n = 600 rpm Radial load, W = 5 kN Let us consider that there is no eccentricity between the bearing and the journal and that there exists a lubricant flow only in the circumferential direction and not in the axial direction With these assumptions, Petroff s equation can be applied Friction Coefficient, f
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