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Ri = 553 lbf s in 5
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233 109 N s m 5
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Fig 661: Capillary restrictor
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Rolling Element, Hydrodynamic and Hydrostatic Bearings Outflow Resistance, Ro rectangular pad
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The outflow resistance is the pressure drop divided by the rate of flow of liquid As the flow through the clearance is usually laminar, the outflow resistance is only dependent on the geometrical shape of the lands, the clearance and the viscosity of the fluid 6 Ro = a b h 3 + 3096 c c Ro =
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8 10 9 6 5 10 6 775 12 2 + 2 3096
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Ro = 553 lbf s in 5 The Resistance Ratio,
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The resistance ratio governs most of the performance characteristics of the hydrostatic bearing For design purposes, the practical values of x can be considered to be in the range of 05 80 x = x =
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Ri Ro 553 553
x = 1
Relation between Supply Pressure, Ps and Pocket Pressure, PR For design conditions, the relation between the supply pressure and the pocket or recess pressure is taken to be PR = PR =
1+ 225 1+1
776 103 N m 2
PR = 112 lbf in 2 Virtual Bearing Area, Av rectangular pad
The pressure distribution over the area of the pocket is nearly constant, but the pressure subsequently drops towards the outer perimeter of the land Therefore, the equivalent area is imagined as an area that is subjected to the same pressure as that of the liquid in the recess that would develop the same thrust as the actual hydrostatic pad
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Fig 662: One-dimensional illustration of actual and virtual pad areas
c c Av = a b 1 a b 2 2 Av = 775 12 1 775 12 2 Av = 535 in 345 10 3 m2
Hydrostatic Thrust, T T = PR Av T = 535 112 T = 6020 lbf Bearing Stiffness, dT/dh capillary inflow restrictor The bearing stiffness is the rate of change of the thrust force with respect to the clearance For design conditions, the hydrostatic bearing stiffness is given as
268 N
The negative sign indicates that the load changes in the opposite sense to the clearance
dT dh dT dh dT dh dT dh
Td hd 1 + 6020 1 = 3 0002 1 + 1
= 3 = 451 106 lbf in 1 = 2010 tonf in 1 790 106 N m 1
Rolling Element, Hydrodynamic and Hydrostatic Bearings Volumetric flow, Q capillary and orifice inflow restrictor For design conditions, the volumetric flow for both capillary and orifice restrictors are similar: Ps Q = Ro (1 + ) 225 Q = 553 (1 + 1 ) Q = 0203 in3 s 1 330 10 6 m3 s 1 Pumping power, Pp capillary and orifice inflow restrictor Pp = QPs Pp = 0203 225 517 W Pp = 458 in lbf s 1 For the 10 pads, the total pumping power is multiplied by the number of pads: nPp = 458 10 nPp = 458 in lbf s 1 nPp 007 hp 517 W Friction force, FL and Friction Power, Pf rectangular pad
The friction force is mainly due to the shearing of the fluid film The force is proportional to the viscosity, relative sliding speed, land area and inversely proportional to the clearance: v 2 2 ( a + b ) c 4c2 + 08584r(int) FL = h FL =
FL = 795 lbf 354 N The friction power is obtained by multiplying the friction force with the sliding speed Pf = FLn Pf = 795 50 Pf = 398 in lbf s 1 449 W For the 10 pads, the total friction power is multiplied by the number of pads nPf = 398 10 nPp = 06 hp 449 W Criterion of the Operating Temperature The average temperature rise per pass of the oil through the system of bearing pads, neglecting heat losses is given by p1 + P f / Q t F 152
5 10 6 50 [79 16 + 0588 ] 2 10 3
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where P and Q are the summations of the contributions of the individual pads of a bearing system, p1 = [lbf in 2], Pf = [J s 1] and Q = [in3 s 1]:
225 + 398 / 0203 152 t 14 F 8 K It is assumed that for the most heavily loaded pad, the clearance decreases to 0001 in and for the minimum load, the clearance does not exceed 0004 in The calculation can be made in a similar manner with the exception of the stiffness because the design condition is no longer valid The relation is given as
t
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