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F h3 P = Pr Q = H f Ap where F is the load on the bearing, lb or N; Q the volume flow rate of oil, in3/s or m3/s; P the pumping power, lbin/s or Nm/s (watts); af the = pad load coefficient, dimensionless; qf the pad flow coefficient, dimensionless; Hf the pad power coefficient, dimensionless; Ap the pad area, in2 or m2; Pr the oil pressure in the recess of the pad, psi or Pa; h the film thickness, in or m and is the dynamic viscosity of the oil, lbs/in2 or Pas Figure 657 shows the typical variation of dimensionless coefficients as a function of the pad geometry for a circular pad with a circular recess As the size of the recess (Rr/R) increases, the loadcarrying capacity increases, as indicated by af But at the same time, the flow through the bearing increases, as indicated by qf The increase is gradual up to a value of Rr/R of approximately 07, and then rapid for higher ratios This higher flow rate requires a much higher pumping power, as indicated by the rapidly increasing power coefficient At very low ratios of Rr/R, the load coefficient decreases rapidly The pressure in the recess would have to increase to compensate in order to lift the load The higher pressure requires more pumping power Therefore, the power coefficient is high at



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Fig 657: Dimensionless coefficients for a circular pad hydrostatic bearing [14]

The quantity that we intend to calculate has a gauge-independent finite part. Indeed, in Eq. (7-45) the term proportional to (1 - A) involves an integral over

larger resistor: R R1 R2 R3 5-5

either very small ratios of Rr/R or at high ratios The minimum power is required for ratios between 04 and 06 [14] Example: Circular Pads Hydrostatic Bearings A large antenna mount weighing 12,000 lb is to be supported on three hydrostatic bearings such that each bearing pad carries 4,000 lb A positive displacement pump will be used to deliver oil at a pressure of up to 500 psi We now design the hydrostatic bearings [14]





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When devices are in parallel, they are connected side-by-side, as shown in Fig. 5-17. Because current has more than one path through the circuit, there is less resistance in a parallel circuit than in one of the resistors in the circuit. For two resistors, the total resistance is: R R1 R2 R1 R2 5-6

From Figure 659, the minimum power required for a circular pad bearing would occur with a ratio (Rr/R) of approximately 050, for which the value of the load coefficient ar = 055 The pressure at the bearing recess will be somewhat below the maximum available of 500 psi because of the pressure drop in the restrictor placed between the supply manifold and the pad The design is completed for a recess pressure of approximately 400 psi F = af Ap Pr Ap = Ap =

4 Ap / 4 (182 ) /

If there are more than two resistors, the general calculation is: R 1 1 1 1 R1 R2 RN 5-7

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D = 481 in 12217 mm For convenience, the diameter, D, is assumed to be 500 in The actual pad area will then be Ap = pD 2/4 Ap = (p) (5)2/4 1264514 mm Ap = 196 in2 R = D/2 = 500/2 = 250 in Rr = 050 R = 050 (250) = 125 in The required recess pressure is then F Pr = a f Ap Pr =

4000 055 196

One application of a resistor network is as a voltage divider, shown in Fig. 5-18. When a voltage is applied across this network, the output voltage

Pr = 370 lb/in2 026 kg /mm2 The clearance, h, is recommended to be between 0001 and 001 in Assume h = 0005 in = 0127 mm The viscosity can be obtained from Figure 634 for a given type of lubricant and temperature In this case, it is assumed that viscosity, = 83 10 6 lbs/in2 qf = 14 (Figure 659) Q = qf

Q = 430 in3/s Hf = 26 (Figure 659)

Fig. 5-18.

4000 00053 196 83 10 6

at the point between the two resistors is a controlled fraction of the input voltage: R2 5-8 Vout Vin R1 R2 If one of the resistors, such as R2, isn t xed but is allowed to change in value, the output voltage will change from some high value to nearly zero depending on the setting. This can then be used as a control value, such as a volume control, or provide the result from an input sensor. A potentiometer, or variable resistor, is often used as a resistor bridge to provide control for electronic devices. On schematics these can be abbreviated pot or labeled trim for trim potentiometers that are used to adjust a circuit.

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